401:
rather than
Hamiltonian formalism, this investigation relied on the S-matrix formulation of Statistical Mechanics developed by R.F. Dashen and S.K. Ma. The criteria derived by Dashen and RR, when applied to the neutron star equation of state, showed that treating the Δ(3-3 ) as an independent elementary particle was a reasonable approximation. Separately Rajaraman studied, with Dashen and Ma, the finite temperature behaviour of the Gross and Neveu model which spontaneously breaks chiral symmetry. Dashen, Ma and Rajaraman found that when temperature is turned on, however slightly, the symmetry is restored. Separately, Ma and Rajaraman gave a pedagogical explanation of when and why broken symmetries are restored by fluctuations. Another intriguing result, obtained with Raj Lakshmi was the symmetry restoration, upon quantisation, of some field theories because of zero-point energy differences.
431:
minimal deterrence and anti-ballistic-missile and early warning systems. He has repeatedly urged capping of India’s nuclear arsenal based on technical and strategic grounds that a small arsenal will suffice to meet the requirements of the Indian government's stated doctrine of minimum deterrence. He has championed nuclear de-alert agreements and other confidence building measures at track II meetings with
Pakistani and Chinese colleagues. He has calculated fissile material production and stocks in South Asia and analysed the prospects for FMCT. More recently argued in favour of India’s joining the Comprehensive Test ban Treaty (CTBT). He has analysed in detail the ramifications of the US-India Nuclear Agreement Nuclear Deal and was an active participant in the contentious public debate surrounding its three-year negotiations (2005–08).
349:
of nucleons, thereby generating a density expansion. He also outlined a method for doing so. Subsequently, Hans Bethe converted
Rajaraman's outline into a substantive theory for the three-nucleon problem in nuclear matter. These developments, summarized in the 1967 review article by Rajaraman with Bethe, eventually led to the Coupled Cluster method in Many Body theory. Subsequently, B.H.J. McKellar, Rajaraman studied the impact on of intrinsic three-body and higher many-body forces between nucleons, (as distinct from the familiar pairwise nuclear forces) on nuclear matter. Separately Rajaraman showed that nucleon-nucleon correlations suppress pion condensation in neutron stars.
463:, published in 1982 by Elsevier North Holland. It explained in simple and coherent manner these developments as well as associated techniques of path integrals, instanton induced vacuum tunnelling, Grassman fields, and multiple gauge vacua. Since these methods have found applications in nuclear, particle and condensed matter physics, this book has been widely used around the world by a generation of theoretical physicists. Its translation rights were bought by the Soviet Press MIR, who published it in Russian in 1985. Subsidized copies of the book were made available to most leading physics departments in the Soviet Union and Eastern Europe.
379:, examined the curious phenomenon of quantum states with fractional fermion number, discovered theoretically by Jackiw and Rebbi and experimentally observed in Polyacetylene. These findings seemed to violate common sense at first sight. Rajaraman and Bell clarified this puzzle, in a pair of papers, one addressing the problem in the continuum Dirac theory, and the other in a lattice model of polyacetylene. They showed that the missing fraction of the electron was lurking at the edges of the system, as has also been seen since then in some experiments.
392:
Rajaraman demonstrated using Dirac’s theory of
Constraints that the presence of a gauge anomaly only alters the constraint structure of the theory so that although it is no longer gauge invariant, but it still remains canonically consistent and relativistic. Later, he went on extend these results to different non-abelian gauge theories in two- and four dimensions, including (with Percacci) the chirally gauged Wess-Zumino-Witten model.
25:
410:
features of
Bilayer quantum hall systems. A.H. MacDonald and T. Jungwirth and Rajaraman constructed their phase diagram at filling factor of two as a function of the Zeeman coupling, the layer bias and interlayer tunneling. They showed its ground state has a rich structure of broken symmetries including one exhibiting canted anti-ferromagnetism.
479:
for his “efforts to promote peace and nuclear security in South Asia though extensive engagements and writings” and the Shanti Swarup
Bhatnagar Prize in Physical Sciences in 1983. He was also recipient of 1989 Dr. G.P. Chatterjee Memorial Award and 1995 S.N.Bose Medal of the Indian National Science
434:
Rajaraman is a founding member and past co-chair of the
International Panel on Fissile Materials, of the Council of the Pugwash Conference on Science & World Affairs, and of the Asia Pacific Leadership Network for Nuclear Non-Proliferation and Disarmament, and a member of the Science and Security
400:
Motivated by neutron-star calculations which treat the Δ(3-3 ) hadron resonance as a separate species of fermions, Rajaraman and R.F. Dashen analysed the general question of the effective elementarity of narrow resonances in hadronic ensembles. Since resonances are naturally described in the S-matrix
348:
In 1962-63, as part of his PhD thesis, Rajaraman demonstrated that the prevalent calculations of the energy of nuclear matter in powers of the
Brueckner reaction matrix would not yield a convergent result. He suggested instead summing, in closed form, interactions to all orders among any given number
422:
Rajaraman has argued against India developing nuclear weapons long before its first nuclear test at
Pokhran in 1974. However even after India and Pakistan officially started building nuclear weapons in 1998, he felt he should stay engaged with the strategic community and strive for nuclear restraint
413:
Rajaraman and PhD student
Sankalpa Ghosh studied topologically non trivial "meron" and bi-meron excitations in layer-spin for bilayer Hall systems taking into account differences in interlayer and intra-layer coulomb energy. They also analyzed CP_{3} solitons arising in a four-component description
365:
With S. Rai Choudhary and G. Rajasekaran, he obtained several results on deep inelastic electron scattering data being then generated at SLAC. These included (i) constraints on its Structure Functions, (ii) its relationship to purely hadronic inclusive scattering (N+N→N+ X) and (iii) discovery of a
409:
Rajaraman and S. L. Sondhi constructed a bosonic field operator for composite bosons, in quantum Hall systems whose condensate yields the Laughlin states at the mean field level. In a similar vein, Rajaraman constructed field operators for Jain’s flux-electron composites. He also studied different
454:
Despite the wide ranging research contributions summarised above, Rajaraman will perhaps be remembered more for his teaching. At all the universities where he has taught for over 50 years, he has been known for his teaching skills in physics, particularly of quantum theory. The same holds for the
445:
He has also written on safety, security and transparency in India’s nuclear energy program, from well before the Fukushima tragedy. To help mitigate the contentious views on nuclear energy among the Indian public, he organised and edited a book on India’s nuclear energy program with contributors
391:
and Rajaraman showed that gauge theories with anomalies are not necessarily inconsistent, contrary to the general belief till then. They solved the Chiral Schwinger Model (CSM), which is anomalous, exactly and proved that it has a consistent and relativistically covariant spectrum. Following this
430:
Since then, through articles, television appearances and lectures at think tanks and universities in India and abroad, Rajaraman has tried to bring clarity to nuclear issues in South Asia and at the global level. His work covers nuclear weapon accidents, civil defense, India’s nuclear doctrine,
458:
Perhaps the most widely known examples of this were his monographs on quantum solitons. A new non-perturbative approach to quantum field theory was being developed in the 1970s by quantizing fluctuations around exact classical (soliton) solutions, to get extended quantum particle states with
357:
During the ‘Seventies, Rajaraman extended his research to include particle physics. At that time, high energy hadron scattering was being analysed using S-matrix and Regge pole techniques. Since the Froissart-Martin asymptotic bounds on hadron scattering is not applicable to Weak Interactions,
361:
Rajaraman gave the first determination from experimental data of the value of the "Triple Pomeron Vertex" as a function of momentum transfer and also derived the consequences of the vanishing of this vertex on high energy hadron scattering. With Finkelstein, he analysed Exchange Degeneracy in
339:
A notable feature of Rajaraman’s research is the diversity of the areas on which he has worked. In theoretical physics his work spanning four decades (1962-2002) covers nuclear many-body theory, elementary particles, quantum field theory, soliton physics, quantum hall effect and aspects of
340:
Statistical Mechanics. In addition, since 2000, he has been deeply engaged in technical and advocative work on public policy, including global nuclear disarmament, India’s civilian and military nuclear programs and higher education. Given below is a summary of some of this work.
374:
Aside from his reviews and his book, Rajaraman’s original results on solitons include exact soliton solutions' of coupled scalar field theories and with E. Weinberg a method for quantizing Solitons with internal symmetries. In 1982, Rajaraman and the theorist
446:
ranging from leaders of the governmental Department of Atomic Energy to anti-nuclear activists. He was a member of the Expert Committee of the Nuclear Threat Initiative (NTI) for developing their 2012 Nuclear Security Index.
423:
and threat reduction To this end, he educated himself more deeply on nuclear technology and policy. In this he was greatly helped by repeated visits to Princeton University’s Program on Science and Global Security, led by
358:
Rajaraman constructed a self-consistent theory of zero-mass neutrinos and showed that ν- ν and ν- ν(bar) scattering total cross sections asymptotically become equal and approach the same constant value.
279:. In addition to his physics publications, Rajaraman has written widely on topics including fissile material production in India and Pakistan and the radiological effects of nuclear weapon accidents.
459:
remarkable topological properties. In 1975 Rajaraman published the very first review article on these new methods in the review journal Physics Reports. Subsequently, he developed it as a book,
2657:
194:
2662:
2632:
271:
Science and Security Board. He has taught and conducted research in physics at the Indian Institute of Science, the Institute for Advanced Study at Princeton, and as a
2321:"The India-US Nuclear Deal: The perspective of a non governmental scientist" in "Canadian Policy on Nuclear Cooperation with India", Ed: Sasikumar and Huntley
2627:
813:
McKellar, Bruce H. J.; Rajaraman, R. (1971). "Effect of Correlations on the Contribution of Three-Body Forces to the Binding Energy of Nuclear Matter".
2437:
1694:
Dashen, Roger F.; Ma, Shang-Keng; Rajaraman, R. (1975). "Finite-temperature behavior of a relativistic field theory with dynamical symmetry breaking".
2524:
490:
262:
2647:
42:
33:
414:
of electrons carrying both spin and layer-spin. These solitons carry nontrivial intertwined windings of real spin and layer degrees of freedom.
304:
455:
numerous mini-courses he has given at summer and winter schools in India and abroad, explaining new advances in theoretical physics research.
2328:
320:
2672:
2667:
2642:
1341:
Karthick Selvan, M.; Panigrahi, Prasanta K. (2016). "Charge fractionalization in oxide heterostructures: A field-theoretical model".
2296:"Prospects for a Fissile Materials Treaty and its Implications for India" in "India and Global Nuclear Disarmament" Ed V.R. Raghavan
1177:
267:
119:
1023:
Finkelstein, J.; Rajaraman, R. (1 February 1972). "Inclusive Experiments, Exchange Degeneracy, and Reggeon Total Cross Sections".
100:
2652:
72:
503:
442:
For his work on nuclear arms control, Rajaraman received the Leo Szilard Award given by the American Physical Society in 2014.
173:
1905:
MacDonald, A. H.; Rajaraman, R.; Jungwirth, T. (1999). "Broken-symmetry ground states in ν = 2 bilayer quantum Hall systems".
49:
883:
Rajaraman, R. (25 February 1969). "Self-Consistent High-Energy Scattering of Zero-Mass Leptons: The Coupled-Channel Case".
79:
472:
308:
2262:"Exploring Uranium Resource Constraints on Fissile Material Production in Pakistan ( with Zia Mian and A. H. Nayyar)".
1659:
Dashen, R. F.; Rajaraman, R. (1974). "Effective elementarity of resonances and bound states in statistical mechanics".
1093:
Choudhury, S. Rai; Rajaraman, R. (1972). "Relationship Between Hadronic and Electronic Excitation of N ∗ Resonances".
918:
Rajaraman, R. (1971). "Evaluation of the Triple-Pomeranchukon-Vertex η PPP ( t ) from Experiment as a Function of t".
312:
258:
226:
2607:
2475:
Rajaraman, R. (1975). "Some non-perturbative semi-classical methods in quantum field theory (a pedagogical review)".
1167:
561:
86:
1729:
Ma, Shang-Keng; Rajaraman, R. (1975). "Comments on the absence of spontaneous symmetry breaking in low dimensions".
1228:
Rajaraman, R.; Weinberg, Erick J. (1975). "Internal symmetry and the semiclassical method in quantum field theory".
988:
Finkelstein, J.; Rajaraman, R. (1971). "Some consequences of exchange degeneracy and the triple-Regge-hypothesis".
496:
2445:
540:
476:
199:
68:
2128:
Mian, Zia; Rajaraman, R.; Ramana, M. V. (2003). "Early Warning in South Asia – Constraints and Implications".
2064:
Ghosh, Sankalpa; Rajaraman, R. (2000). "Quantum Hall solitons with intertwined spin and pseudospin at ν = 1".
536:
Member, Permanent Monitoring Panel—Mitigation of Terrorist Acts, World Federation of Scientists, Erice, Italy
2450:
1585:
Percacci, R.; Rajaraman, R. (1988). "Gauss law commutator in the chirally gauged Wess-Zumino-Witten model".
315:, Bangalore (1976–93), finally JNU (1994- ) where he is now Emeritus Professor. He spent sabbaticals at the
38:
2637:
2579:
307:
in 1963, he returned to Cornell to teach and continue research. In 1969, after spending two years at the
2412:"There is no Real Debate on Our Nuclear Programme". The Times of India ( Editorial Page). 28 April 1988.
275:
at Stanford, Harvard, MIT, and elsewhere. He received his doctorate in theoretical physics in 1963 from
1852:
Rajaraman, R. (1997). "Generalized Chern-Simons theory of composite fermions in bilayer Hall systems".
848:
Rajaraman, R. (February 1974). "Effect of nucleon correlations on pion condensation in neutron stars".
2282:"" India and the FMCT", Country Perspectives on the Challenges to a Fissile materials (Cutoff) Treaty"
1058:
Choudhury, S. Rai; Rajaraman, R. (1970). "Constraint on the Universal Function in Electroproduction".
2622:
2484:
2228:
2137:
2083:
2030:
1977:
1924:
1871:
1818:
1773:
1738:
1703:
1668:
1633:
1594:
1559:
1520:
1485:
1446:
1403:
1360:
1315:
1276:
1237:
1202:
1137:
1102:
1067:
1032:
997:
962:
927:
892:
857:
822:
787:
752:
713:
678:
643:
292:
953:
Rajaraman, R. (July 1972). "Some consequences of the vanishing of the triple-pomeronchukon-vertex".
324:
254:
2244:
2153:
2099:
2073:
2046:
2020:
1993:
1967:
1940:
1914:
1887:
1861:
1834:
1808:
1376:
1350:
316:
296:
276:
272:
180:
93:
2324:
1419:
1173:
376:
1958:
Ghosh, Sankalpa; Rajaraman, R. (1998). "Meron Pseudospin Solutions in Quantum Hall Systems".
2492:
2236:
2232:
2145:
2141:
2091:
2038:
1985:
1932:
1879:
1826:
1781:
1746:
1711:
1676:
1641:
1621:
1602:
1567:
1528:
1493:
1454:
1411:
1368:
1323:
1284:
1245:
1210:
1145:
1110:
1075:
1040:
1005:
970:
935:
900:
865:
830:
795:
760:
740:
721:
686:
651:
424:
288:
233:
2117:
R, Rajaraman (12 July 1970). "The Unclear Nuclear Debate". The Illustrated Weekly of India.
1764:
Rajaraman, R.; Lakshmi, M. Raj (1981). "Restoration of symmetry by radiative corrections".
669:
Rajaraman, R. (1963). "Three-Body Effect in Nuclear Matter to All Orders of Perturbation".
1128:
Rajaraman, R.; Rajasekaran, G. (1971). "Fixed Pole in the Virtual Compton Amplitude A 2".
57:
2565:
1437:
Rajaraman, R. (1985). "Hamiltonian formulation of the anomalous chiral Schwinger model".
2488:
2087:
2034:
2011:
Ghosh, Sankalpa; Rajaraman, R. (1998). "Bimerons in Double Layer Quantum Hall Systems".
1981:
1928:
1875:
1822:
1777:
1742:
1707:
1672:
1637:
1598:
1563:
1524:
1489:
1450:
1407:
1364:
1319:
1280:
1241:
1206:
1141:
1106:
1071:
1036:
1001:
966:
931:
896:
861:
826:
791:
756:
717:
682:
647:
1394:
Jackiw, R.; Rajaraman, R. (1985). "Vector-Meson Mass Generation by Chiral Anomalies".
2616:
2496:
2157:
2050:
1944:
1838:
1606:
1571:
1532:
1497:
1458:
1380:
1327:
1288:
1193:
Rajaraman, R. (1979). "Solitons of Coupled Scalar Field Theories in Two Dimensions".
1009:
974:
869:
311:
at Princeton he returned to India, working first at Delhi University (1969–76), then
2248:
2103:
1997:
1891:
1372:
778:
McKellar, Bruce H. J.; Rajaraman, R. (1968). "Three-Body Forces in Nuclear Matter".
388:
616:
2344:
1415:
52:. Contentious material about living persons that is unsourced or poorly sourced
24:
2309:"It Is Time India Signs the Nuclear Test Ban Treaty". The Wire. 6 January 2017.
2193:"Minimum Deterrent and Large Arsenal". The Hindu (Editorial Page). 2 July 2014.
2095:
1214:
939:
799:
2240:
2042:
1989:
1830:
764:
300:
238:
1936:
1883:
1799:
Rajaraman, R.; Sondhi, S. L. (1996). "A Field Theory for the Read Operator".
1785:
1750:
1715:
1249:
904:
725:
690:
1680:
1645:
1079:
834:
655:
591:
331:, University of Illinois and the Institute for Advanced Study in Princeton.
2426:. Academic Foundation and Indian National Science Academy, New Delhi. 2013.
2171:"Cap the Nuclear Arsenal Now". The Hindu (Editorial Page). 25 January 2005.
1511:
Rajaraman, R. (1987). "On anomalous U(1) gauge theory in four dimensions".
1423:
1149:
1114:
1044:
569:
2078:
2025:
1972:
1919:
1866:
1813:
489:
Founding member (2006–present) and past Co-Chairman (2007-2014) of the
216:
2323:. Simons Centre for Disarmament and Non-Proliferation Research. 2007.
2219:
Rajaraman, R. (2008). "Estimates of India's Fissile Material Stocks".
2149:
2546:
1548:"Degrees of freedom and the quantization of anomalous gauge theories"
1547:
1473:
1303:
1264:
1355:
2370:
2281:
1169:
An Introduction to Solitons and Instantons in Quantum Field Theory
704:
Bethe, H. A. (1965). "Three-Body Correlations in Nuclear Matter".
634:
Rajaraman, R. (1963). "Three-Nucleon Clusters in Nuclear Matter".
506:, elected 1985, council member (2004–06), Vice-President (2010–12)
328:
2182:"Nuclear Posture". The Hindu (Editorial Page). 7 February 2003.
18:
2548:
Handbook of Shanti Swarup Bhatnagar Prize Winners (1958–1988)
2384:
2580:"Permanent Monitoring Panel - Mitigation of Terrorist Acts"
2554:. Council of Scientific & Industrial Research. 1999.
2298:. Macmillan Publishers India Ltd. 2010. pp. 77–105.
362:
inclusive reactions involving the triple-Reggeon vertex
2398:
2264:
Science and Global Security ( Gordon and Breach (U.K.))
303:
as his supervisor. After a brief postdoctoral stint at
1474:"Anomalous non-abelian gauge theory in two dimensions"
2221:
Science and Global Security (Gordon and Breach, U.K.)
1304:"On states, on a lattice, with half-integral charge"
2204:"India's Arms Control Quandary (Invited Article)".
232:
222:
212:
189:
169:
161:
143:
136:
2424:"India's Nuclear Energy programme" Ed: R.Rajaraman
516:Council member, Pugwash Conferences (2016–present)
2658:Academic staff of the Indian Institute of Science
253:(born 11 March 1939) is an emeritus professor of
16:Scientist with a doctorate in theoretical physics
2663:Institute for Advanced Study visiting scholars
2525:"2014 Leo Szilard Lectureship Award Recipient"
2513:. Mir Press ( Moscow) and North Holland. 1985.
1161:
1159:
2633:Academic staff of Jawaharlal Nehru University
519:Member of the Asia Pacific Leadership Network
8:
1622:"Narrow resonances in statistical mechanics"
522:Member of the Science and Security Board of
287:Rajaraman completed his BSc (Honours) from
2449:. January 2012. p. 86. Archived from
2438:"About the international panel of experts"
2371:"International Panel on Fissile Materials"
2136:(2–3). Gordon and Breach (U.K.): 109–150.
366:fixed pole in virtual Compton Scattering.
133:
2077:
2024:
2013:International Journal of Modern Physics B
1971:
1960:International Journal of Modern Physics B
1918:
1865:
1812:
1801:International Journal of Modern Physics B
1354:
120:Learn how and when to remove this message
2349:International Panel on Fissile Materials
539:Member, NTI Verification Pilot Project,
533:, (Taylor & Francis publishers, USA)
491:International Panel on Fissile Materials
263:International Panel on Fissile Materials
1265:"On solitons with half integral charge"
553:
2566:"Editors -Science and Global Security"
741:"Three-Body Problem in Nuclear Matter"
353:Regge poles and particle phenomenology
257:at the School of Physical Sciences at
198:2014 Leo Szilard Lectureship Award by
2206:The Bulletin of the Atomic Scientists
1620:Dashen, R. F.; Rajaraman, R. (1974).
261:. He was also the co-Chairman of the
7:
739:Rajaraman, R.; Bethe, H. A. (1967).
427:, a leader on nuclear arms control.
295:in theoretical physics in 1963 from
2385:"Bulletin of the Atomic Scientists"
511:PRAMANA - Indian Journal of Physics
2628:Indian condensed matter physicists
2208:(March–April Issue (2010)): 27–36.
1302:Bell, J.S.; Rajaraman, R. (1983).
1263:Rajaraman, R.; Bell, J.S. (1982).
335:Academic and research achievements
313:Indian Institute of Science (IISc)
268:Bulletin of the Atomic Scientists'
14:
524:Bulletin of the Atomic Scientists
437:Bulletin of the Atomic Scientists
1546:Lott, J.; Rajaraman, R. (1985).
596:The Institute for Advanced Study
471:He is the recipient of the 2014
23:
504:Indian National Science Academy
418:Nuclear policy and arms control
2648:20th-century Indian physicists
1172:. North Holland. p. 418.
195:Shanti Swarup Bhatnagar Prize
1:
2284:. IPFM Report September 2008.
1166:Rajaraman, R (1 April 1987).
473:Leo Szilard Lectureship Award
50:secondary or tertiary sources
2608:Faculty profile of Rajaraman
2497:10.1016/0370-1573(75)90016-2
2399:"A-PLN - Leadership Network"
1607:10.1016/0370-2693(88)90224-9
1572:10.1016/0370-2693(85)91238-9
1533:10.1016/0370-2693(87)90182-1
1498:10.1016/0370-2693(85)91077-9
1459:10.1016/0370-2693(85)90369-7
1328:10.1016/0550-3213(83)90130-X
1289:10.1016/0370-2693(82)90996-0
1010:10.1016/0370-2693(71)90529-6
975:10.1016/0370-2693(72)90828-3
870:10.1016/0370-2693(74)90003-3
309:Institute for Advanced Study
174:St. Stephen's College, Delhi
56:, especially if potentially
34:biography of a living person
2673:People associated with CERN
2527:. American Physical Society
2130:Science and Global Security
1416:10.1103/PhysRevLett.54.1219
1373:10.1209/0295-5075/114/67005
531:Science and Global Security
259:Jawaharlal Nehru University
227:Jawaharlal Nehru University
54:must be removed immediately
2689:
2668:Indian particle physicists
2584:federationofscientists.org
2096:10.1103/PhysRevB.63.035304
1215:10.1103/PhysRevLett.42.200
940:10.1103/PhysRevLett.27.693
800:10.1103/PhysRevLett.21.450
529:Member, Board of Editors,
497:Indian Academy of Sciences
2643:Cornell University alumni
2446:Nuclear Threat Initiative
2270:(2 and 3 (2009)): 77–109.
2241:10.1080/08929880802570248
2043:10.1142/S0217979298001460
1990:10.1142/S021797929800003X
1831:10.1142/S0217979296000337
765:10.1103/RevModPhys.39.745
745:Reviews of Modern Physics
541:Nuclear Threat Initiative
477:American Physical Society
244:
205:
200:American Physical Society
1937:10.1103/PhysRevB.60.8817
1884:10.1103/PhysRevB.56.6788
1786:10.1103/PhysRevD.23.2399
1751:10.1103/PhysRevD.11.1701
1716:10.1103/PhysRevD.11.1499
1250:10.1103/PhysRevD.11.2950
905:10.1103/PhysRev.178.2221
726:10.1103/PhysRev.138.B804
691:10.1103/PhysRev.131.1244
344:Nuclear many-body theory
283:Early life and education
2653:Delhi University alumni
2233:2008S&GS...16...74R
2142:2003S&GS...11..109M
1681:10.1103/PhysRevD.10.708
1646:10.1103/PhysRevD.10.694
1396:Physical Review Letters
1195:Physical Review Letters
1080:10.1103/PhysRevD.2.2728
920:Physical Review Letters
835:10.1103/PhysRevC.3.1877
780:Physical Review Letters
656:10.1103/PhysRev.129.265
484:Fellowships/memberships
461:Solitons and Instantons
439:for six years (see ).
1472:Rajaraman, R. (1985).
1150:10.1103/PhysRevD.3.266
1115:10.1103/PhysRevD.5.773
1045:10.1103/PhysRevD.5.672
526:(2012-2015; 2015-2018)
48:Please help by adding
2511:Солитоны и Инстаптоны
617:"Ramamurti Rajaraman"
396:Statistical mechanics
69:"Ramamurti Rajaraman"
592:"Prof. R. RAJARAMAN"
572:on 30 September 2015
562:"Prof. R. RAJARAMAN"
265:and a member of the
2489:1975PhR....21..227R
2456:on 14 February 2014
2227:(3): 74–87 (2008).
2088:2000PhRvB..63c5304G
2035:1998IJMPB..12.2495G
1982:1998IJMPB..12...37G
1929:1999PhRvB..60.8817M
1876:1997PhRvB..56.6788R
1823:1996IJMPB..10..793R
1778:1981PhRvD..23.2399R
1743:1975PhRvD..11.1701M
1708:1975PhRvD..11.1499D
1673:1974PhRvD..10..708D
1638:1974PhRvD..10..694D
1599:1988PhLB..201..256P
1564:1985PhLB..165..321L
1525:1987PhLB..184..369R
1490:1985PhLB..162..148R
1451:1985PhLB..154..305R
1408:1985PhRvL..54.1219J
1365:2016EL....11467005K
1343:Europhysics Letters
1320:1983NuPhB.220....1B
1281:1982PhLB..116..151R
1242:1975PhRvD..11.2950R
1207:1979PhRvL..42..200R
1142:1971PhRvD...3..266R
1107:1972PhRvD...5..773C
1072:1970PhRvD...2.2728C
1037:1972PhRvD...5..672F
1002:1971PhLB...36..459F
967:1972PhLB...40..392R
932:1971PhRvL..27..693R
897:1969PhRv..178.2221R
862:1974PhLB...48..179R
827:1971PhRvC...3.1877M
792:1968PhRvL..21..450M
757:1967RvMP...39..745R
718:1965PhRv..138..804B
683:1963PhRv..131.1244R
648:1963PhRv..129..265R
405:Quantum hall effect
325:Stanford University
255:theoretical physics
251:Ramamurti Rajaraman
138:Ramamurti Rajaraman
37:relies too much on
467:Honours and awards
317:Harvard University
297:Cornell University
277:Cornell University
273:visiting professor
181:Cornell University
2330:978-1-4303-0811-9
2150:10.1080/714041033
2066:Physical Review B
1907:Physical Review B
1854:Physical Review B
1766:Physical Review D
1731:Physical Review D
1696:Physical Review D
1661:Physical Review D
1626:Physical Review D
1587:Physics Letters B
1552:Physics Letters B
1513:Physics Letters B
1478:Physics Letters B
1439:Physics Letters B
1402:(12): 1219–1221.
1308:Nuclear Physics B
1269:Physics Letters B
1230:Physical Review D
1130:Physical Review D
1095:Physical Review D
1060:Physical Review D
1025:Physical Review D
990:Physics Letters B
955:Physics Letters B
850:Physics Letters B
815:Physical Review C
248:
247:
207:Scientific career
185:
178:
130:
129:
122:
104:
2680:
2595:
2594:
2592:
2590:
2576:
2570:
2569:
2562:
2556:
2555:
2553:
2543:
2537:
2536:
2534:
2532:
2521:
2515:
2514:
2507:
2501:
2500:
2472:
2466:
2465:
2463:
2461:
2455:
2442:
2434:
2428:
2427:
2420:
2414:
2413:
2409:
2403:
2402:
2395:
2389:
2388:
2381:
2375:
2374:
2367:
2361:
2360:
2358:
2356:
2341:
2335:
2334:
2317:
2311:
2310:
2306:
2300:
2299:
2292:
2286:
2285:
2278:
2272:
2271:
2259:
2253:
2252:
2216:
2210:
2209:
2201:
2195:
2194:
2190:
2184:
2183:
2179:
2173:
2172:
2168:
2162:
2161:
2125:
2119:
2118:
2114:
2108:
2107:
2081:
2079:cond-mat/0001226
2061:
2055:
2054:
2028:
2026:cond-mat/9807275
2008:
2002:
2001:
1975:
1973:cond-mat/9711137
1955:
1949:
1948:
1922:
1920:cond-mat/9903318
1902:
1896:
1895:
1869:
1867:cond-mat/9702076
1849:
1843:
1842:
1816:
1814:cond-mat/9601125
1796:
1790:
1789:
1761:
1755:
1754:
1726:
1720:
1719:
1691:
1685:
1684:
1656:
1650:
1649:
1617:
1611:
1610:
1582:
1576:
1575:
1543:
1537:
1536:
1508:
1502:
1501:
1469:
1463:
1462:
1434:
1428:
1427:
1391:
1385:
1384:
1358:
1338:
1332:
1331:
1299:
1293:
1292:
1260:
1254:
1253:
1225:
1219:
1218:
1190:
1184:
1183:
1163:
1154:
1153:
1125:
1119:
1118:
1090:
1084:
1083:
1055:
1049:
1048:
1020:
1014:
1013:
985:
979:
978:
950:
944:
943:
915:
909:
908:
891:(5): 2221–2225.
880:
874:
873:
845:
839:
838:
810:
804:
803:
775:
769:
768:
736:
730:
729:
701:
695:
694:
666:
660:
659:
631:
625:
624:
613:
607:
606:
604:
602:
588:
582:
581:
579:
577:
568:. Archived from
558:
425:Frank von Hippel
291:in 1958 and his
289:Delhi University
234:Doctoral advisor
183:
176:
157:
153:
151:
134:
125:
118:
114:
111:
105:
103:
62:
27:
19:
2688:
2687:
2683:
2682:
2681:
2679:
2678:
2677:
2613:
2612:
2604:
2599:
2598:
2588:
2586:
2578:
2577:
2573:
2564:
2563:
2559:
2551:
2545:
2544:
2540:
2530:
2528:
2523:
2522:
2518:
2509:
2508:
2504:
2477:Physics Reports
2474:
2473:
2469:
2459:
2457:
2453:
2440:
2436:
2435:
2431:
2422:
2421:
2417:
2411:
2410:
2406:
2397:
2396:
2392:
2383:
2382:
2378:
2369:
2368:
2364:
2354:
2352:
2351:. 3 August 2016
2343:
2342:
2338:
2331:
2319:
2318:
2314:
2308:
2307:
2303:
2294:
2293:
2289:
2280:
2279:
2275:
2261:
2260:
2256:
2218:
2217:
2213:
2203:
2202:
2198:
2192:
2191:
2187:
2181:
2180:
2176:
2170:
2169:
2165:
2127:
2126:
2122:
2116:
2115:
2111:
2063:
2062:
2058:
2010:
2009:
2005:
1957:
1956:
1952:
1904:
1903:
1899:
1851:
1850:
1846:
1798:
1797:
1793:
1763:
1762:
1758:
1728:
1727:
1723:
1693:
1692:
1688:
1658:
1657:
1653:
1619:
1618:
1614:
1584:
1583:
1579:
1545:
1544:
1540:
1510:
1509:
1505:
1471:
1470:
1466:
1436:
1435:
1431:
1393:
1392:
1388:
1340:
1339:
1335:
1301:
1300:
1296:
1262:
1261:
1257:
1227:
1226:
1222:
1192:
1191:
1187:
1180:
1165:
1164:
1157:
1127:
1126:
1122:
1092:
1091:
1087:
1057:
1056:
1052:
1022:
1021:
1017:
987:
986:
982:
952:
951:
947:
917:
916:
912:
885:Physical Review
882:
881:
877:
847:
846:
842:
812:
811:
807:
777:
776:
772:
738:
737:
733:
706:Physical Review
703:
702:
698:
671:Physical Review
668:
667:
663:
636:Physical Review
633:
632:
628:
621:thebulletin.org
615:
614:
610:
600:
598:
590:
589:
585:
575:
573:
560:
559:
555:
550:
543:, Washington DC
486:
469:
452:
420:
407:
398:
385:
383:Gauge anomalies
372:
355:
346:
337:
285:
197:
179:
170:Alma mater
155:
149:
147:
139:
126:
115:
109:
106:
63:
61:
47:
43:primary sources
28:
17:
12:
11:
5:
2686:
2684:
2676:
2675:
2670:
2665:
2660:
2655:
2650:
2645:
2640:
2635:
2630:
2625:
2615:
2614:
2611:
2610:
2603:
2602:External links
2600:
2597:
2596:
2571:
2557:
2538:
2516:
2502:
2483:(5): 227–313.
2467:
2429:
2415:
2404:
2390:
2376:
2362:
2336:
2329:
2312:
2301:
2287:
2273:
2254:
2211:
2196:
2185:
2174:
2163:
2120:
2109:
2056:
2003:
1950:
1897:
1844:
1791:
1756:
1721:
1686:
1651:
1612:
1577:
1538:
1503:
1464:
1429:
1386:
1333:
1294:
1255:
1220:
1185:
1178:
1155:
1120:
1085:
1050:
1031:(3): 672–678.
1015:
980:
961:(3): 392–396.
945:
910:
875:
856:(3): 179–182.
840:
805:
770:
731:
696:
661:
626:
608:
583:
552:
551:
549:
546:
545:
544:
537:
534:
527:
520:
517:
514:
507:
500:
499:, elected 1978
493:
485:
482:
468:
465:
451:
448:
419:
416:
406:
403:
397:
394:
384:
381:
371:
368:
354:
351:
345:
342:
336:
333:
284:
281:
246:
245:
242:
241:
236:
230:
229:
224:
220:
219:
214:
210:
209:
203:
202:
191:
187:
186:
171:
167:
166:
163:
159:
158:
145:
141:
140:
137:
128:
127:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
2685:
2674:
2671:
2669:
2666:
2664:
2661:
2659:
2656:
2654:
2651:
2649:
2646:
2644:
2641:
2639:
2638:Living people
2636:
2634:
2631:
2629:
2626:
2624:
2621:
2620:
2618:
2609:
2606:
2605:
2601:
2585:
2581:
2575:
2572:
2567:
2561:
2558:
2550:
2549:
2542:
2539:
2526:
2520:
2517:
2512:
2506:
2503:
2498:
2494:
2490:
2486:
2482:
2478:
2471:
2468:
2452:
2448:
2447:
2439:
2433:
2430:
2425:
2419:
2416:
2408:
2405:
2400:
2394:
2391:
2386:
2380:
2377:
2372:
2366:
2363:
2350:
2346:
2340:
2337:
2332:
2326:
2322:
2316:
2313:
2305:
2302:
2297:
2291:
2288:
2283:
2277:
2274:
2269:
2265:
2258:
2255:
2250:
2246:
2242:
2238:
2234:
2230:
2226:
2222:
2215:
2212:
2207:
2200:
2197:
2189:
2186:
2178:
2175:
2167:
2164:
2159:
2155:
2151:
2147:
2143:
2139:
2135:
2131:
2124:
2121:
2113:
2110:
2105:
2101:
2097:
2093:
2089:
2085:
2080:
2075:
2072:(3): 035304.
2071:
2067:
2060:
2057:
2052:
2048:
2044:
2040:
2036:
2032:
2027:
2022:
2018:
2014:
2007:
2004:
1999:
1995:
1991:
1987:
1983:
1979:
1974:
1969:
1965:
1961:
1954:
1951:
1946:
1942:
1938:
1934:
1930:
1926:
1921:
1916:
1912:
1908:
1901:
1898:
1893:
1889:
1885:
1881:
1877:
1873:
1868:
1863:
1859:
1855:
1848:
1845:
1840:
1836:
1832:
1828:
1824:
1820:
1815:
1810:
1806:
1802:
1795:
1792:
1787:
1783:
1779:
1775:
1771:
1767:
1760:
1757:
1752:
1748:
1744:
1740:
1736:
1732:
1725:
1722:
1717:
1713:
1709:
1705:
1701:
1697:
1690:
1687:
1682:
1678:
1674:
1670:
1666:
1662:
1655:
1652:
1647:
1643:
1639:
1635:
1631:
1627:
1623:
1616:
1613:
1608:
1604:
1600:
1596:
1592:
1588:
1581:
1578:
1573:
1569:
1565:
1561:
1557:
1553:
1549:
1542:
1539:
1534:
1530:
1526:
1522:
1518:
1514:
1507:
1504:
1499:
1495:
1491:
1487:
1483:
1479:
1475:
1468:
1465:
1460:
1456:
1452:
1448:
1444:
1440:
1433:
1430:
1425:
1421:
1417:
1413:
1409:
1405:
1401:
1397:
1390:
1387:
1382:
1378:
1374:
1370:
1366:
1362:
1357:
1352:
1348:
1344:
1337:
1334:
1329:
1325:
1321:
1317:
1313:
1309:
1305:
1298:
1295:
1290:
1286:
1282:
1278:
1274:
1270:
1266:
1259:
1256:
1251:
1247:
1243:
1239:
1235:
1231:
1224:
1221:
1216:
1212:
1208:
1204:
1200:
1196:
1189:
1186:
1181:
1179:9780444870476
1175:
1171:
1170:
1162:
1160:
1156:
1151:
1147:
1143:
1139:
1135:
1131:
1124:
1121:
1116:
1112:
1108:
1104:
1100:
1096:
1089:
1086:
1081:
1077:
1073:
1069:
1065:
1061:
1054:
1051:
1046:
1042:
1038:
1034:
1030:
1026:
1019:
1016:
1011:
1007:
1003:
999:
995:
991:
984:
981:
976:
972:
968:
964:
960:
956:
949:
946:
941:
937:
933:
929:
925:
921:
914:
911:
906:
902:
898:
894:
890:
886:
879:
876:
871:
867:
863:
859:
855:
851:
844:
841:
836:
832:
828:
824:
820:
816:
809:
806:
801:
797:
793:
789:
785:
781:
774:
771:
766:
762:
758:
754:
750:
746:
742:
735:
732:
727:
723:
719:
715:
711:
707:
700:
697:
692:
688:
684:
680:
676:
672:
665:
662:
657:
653:
649:
645:
641:
637:
630:
627:
622:
618:
612:
609:
597:
593:
587:
584:
571:
567:
563:
557:
554:
547:
542:
538:
535:
532:
528:
525:
521:
518:
515:
512:
508:
505:
501:
498:
494:
492:
488:
487:
483:
481:
478:
474:
466:
464:
462:
456:
449:
447:
443:
440:
438:
435:Board of the
432:
428:
426:
417:
415:
411:
404:
402:
395:
393:
390:
382:
380:
378:
369:
367:
363:
359:
352:
350:
343:
341:
334:
332:
330:
326:
322:
318:
314:
310:
306:
302:
298:
294:
290:
282:
280:
278:
274:
270:
269:
264:
260:
256:
252:
243:
240:
237:
235:
231:
228:
225:
221:
218:
215:
211:
208:
204:
201:
196:
192:
188:
182:
175:
172:
168:
164:
160:
156:(age 85)
154:11 March 1939
146:
142:
135:
132:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
51:
45:
44:
40:
35:
30:
26:
21:
20:
2589:29 September
2587:. Retrieved
2583:
2574:
2560:
2547:
2541:
2531:18 September
2529:. Retrieved
2519:
2510:
2505:
2480:
2476:
2470:
2458:. Retrieved
2451:the original
2444:
2432:
2423:
2418:
2407:
2393:
2379:
2365:
2353:. Retrieved
2348:
2339:
2320:
2315:
2304:
2295:
2290:
2276:
2267:
2263:
2257:
2224:
2220:
2214:
2205:
2199:
2188:
2177:
2166:
2133:
2129:
2123:
2112:
2069:
2065:
2059:
2019:(24): 2495.
2016:
2012:
2006:
1963:
1959:
1953:
1913:(12): 8817.
1910:
1906:
1900:
1860:(11): 6788.
1857:
1853:
1847:
1804:
1800:
1794:
1772:(10): 2399.
1769:
1765:
1759:
1734:
1730:
1724:
1699:
1695:
1689:
1664:
1660:
1654:
1629:
1625:
1615:
1590:
1586:
1580:
1558:(4–6): 321.
1555:
1551:
1541:
1516:
1512:
1506:
1484:(1–3): 148.
1481:
1477:
1467:
1442:
1438:
1432:
1399:
1395:
1389:
1349:(6): 67005.
1346:
1342:
1336:
1311:
1307:
1297:
1275:(2–3): 151.
1272:
1268:
1258:
1236:(10): 2950.
1233:
1229:
1223:
1198:
1194:
1188:
1168:
1133:
1129:
1123:
1098:
1094:
1088:
1066:(11): 2728.
1063:
1059:
1053:
1028:
1024:
1018:
993:
989:
983:
958:
954:
948:
923:
919:
913:
888:
884:
878:
853:
849:
843:
818:
814:
808:
783:
779:
773:
748:
744:
734:
712:(4B): B804.
709:
705:
699:
674:
670:
664:
639:
635:
629:
620:
611:
601:29 September
599:. Retrieved
595:
586:
576:29 September
574:. Retrieved
570:the original
565:
556:
530:
523:
510:
470:
460:
457:
453:
444:
441:
436:
433:
429:
421:
412:
408:
399:
386:
373:
364:
360:
356:
347:
338:
286:
266:
250:
249:
223:Institutions
206:
131:
116:
107:
97:
90:
83:
76:
64:
53:
36:
2623:1939 births
1737:(6): 1701.
1702:(6): 1499.
926:(10): 693.
821:(5): 1877.
677:(3): 1244.
513:(1989-1992)
162:Nationality
60:or harmful.
2617:Categories
1807:(7): 793.
1667:(2): 708.
1632:(2): 694.
1593:(2): 256.
1519:(4): 369.
1445:(4): 305.
1356:1603.05590
1201:(4): 200.
1136:(1): 266.
1101:(3): 773.
996:(5): 459.
786:(7): 450.
751:(4): 745.
642:(1): 265.
548:References
301:Hans Bethe
239:Hans Bethe
150:1939-03-11
110:March 2019
80:newspapers
39:references
2460:14 August
2345:"Members"
2158:119571308
2051:119354403
1966:(1): 37.
1945:119411013
1839:119091796
1381:119216386
480:Academy.
475:from the
389:R. Jackiw
387:In 1985,
377:John Bell
2249:10258879
2104:15427095
1998:15964684
1892:14873601
1424:10030968
1314:(1): 1.
509:Editor,
502:Fellow,
495:Fellow,
450:Teaching
370:Solitons
58:libelous
2485:Bibcode
2355:1 April
2229:Bibcode
2138:Bibcode
2084:Bibcode
2031:Bibcode
1978:Bibcode
1925:Bibcode
1872:Bibcode
1819:Bibcode
1774:Bibcode
1739:Bibcode
1704:Bibcode
1669:Bibcode
1634:Bibcode
1595:Bibcode
1560:Bibcode
1521:Bibcode
1486:Bibcode
1447:Bibcode
1404:Bibcode
1361:Bibcode
1316:Bibcode
1277:Bibcode
1238:Bibcode
1203:Bibcode
1138:Bibcode
1103:Bibcode
1068:Bibcode
1033:Bibcode
998:Bibcode
963:Bibcode
928:Bibcode
893:Bibcode
858:Bibcode
823:Bibcode
788:Bibcode
753:Bibcode
714:Bibcode
679:Bibcode
644:Bibcode
217:Physics
177:(B.Sc.)
94:scholar
2327:
2247:
2156:
2102:
2049:
1996:
1943:
1890:
1837:
1422:
1379:
1176:
213:Fields
190:Awards
165:Indian
96:
89:
82:
75:
67:
2552:(PDF)
2454:(PDF)
2441:(PDF)
2245:S2CID
2154:S2CID
2100:S2CID
2074:arXiv
2047:S2CID
2021:arXiv
1994:S2CID
1968:arXiv
1941:S2CID
1915:arXiv
1888:S2CID
1862:arXiv
1835:S2CID
1809:arXiv
1377:S2CID
1351:arXiv
299:with
193:1983
184:(PhD)
101:JSTOR
87:books
32:This
2591:2015
2533:2015
2462:2023
2357:2019
2325:ISBN
1420:PMID
1174:ISBN
603:2015
578:2015
329:CERN
305:TIFR
144:Born
73:news
2493:doi
2237:doi
2146:doi
2092:doi
2039:doi
1986:doi
1933:doi
1880:doi
1827:doi
1782:doi
1747:doi
1712:doi
1677:doi
1642:doi
1603:doi
1591:201
1568:doi
1556:165
1529:doi
1517:184
1494:doi
1482:162
1455:doi
1443:154
1412:doi
1369:doi
1347:114
1324:doi
1312:220
1285:doi
1273:116
1246:doi
1211:doi
1146:doi
1111:doi
1076:doi
1041:doi
1006:doi
971:doi
936:doi
901:doi
889:178
866:doi
831:doi
796:doi
761:doi
722:doi
710:138
687:doi
675:131
652:doi
640:129
566:jnu
321:MIT
293:PhD
41:to
2619::
2582:.
2491:.
2481:21
2479:.
2443:.
2347:.
2268:17
2266:.
2243:.
2235:.
2225:16
2223:.
2152:.
2144:.
2134:11
2132:.
2098:.
2090:.
2082:.
2070:63
2068:.
2045:.
2037:.
2029:.
2017:12
2015:.
1992:.
1984:.
1976:.
1964:12
1962:.
1939:.
1931:.
1923:.
1911:60
1909:.
1886:.
1878:.
1870:.
1858:56
1856:.
1833:.
1825:.
1817:.
1805:10
1803:.
1780:.
1770:23
1768:.
1745:.
1735:11
1733:.
1710:.
1700:11
1698:.
1675:.
1665:10
1663:.
1640:.
1630:10
1628:.
1624:.
1601:.
1589:.
1566:.
1554:.
1550:.
1527:.
1515:.
1492:.
1480:.
1476:.
1453:.
1441:.
1418:.
1410:.
1400:54
1398:.
1375:.
1367:.
1359:.
1345:.
1322:.
1310:.
1306:.
1283:.
1271:.
1267:.
1244:.
1234:11
1232:.
1209:.
1199:42
1197:.
1158:^
1144:.
1132:.
1109:.
1097:.
1074:.
1062:.
1039:.
1027:.
1004:.
994:36
992:.
969:.
959:40
957:.
934:.
924:27
922:.
899:.
887:.
864:.
854:48
852:.
829:.
817:.
794:.
784:21
782:.
759:.
749:39
747:.
743:.
720:.
708:.
685:.
673:.
650:.
638:.
619:.
594:.
564:.
327:,
323:,
319:,
152:)
2593:.
2568:.
2535:.
2499:.
2495::
2487::
2464:.
2401:.
2387:.
2373:.
2359:.
2333:.
2251:.
2239::
2231::
2160:.
2148::
2140::
2106:.
2094::
2086::
2076::
2053:.
2041::
2033::
2023::
2000:.
1988::
1980::
1970::
1947:.
1935::
1927::
1917::
1894:.
1882::
1874::
1864::
1841:.
1829::
1821::
1811::
1788:.
1784::
1776::
1753:.
1749::
1741::
1718:.
1714::
1706::
1683:.
1679::
1671::
1648:.
1644::
1636::
1609:.
1605::
1597::
1574:.
1570::
1562::
1535:.
1531::
1523::
1500:.
1496::
1488::
1461:.
1457::
1449::
1426:.
1414::
1406::
1383:.
1371::
1363::
1353::
1330:.
1326::
1318::
1291:.
1287::
1279::
1252:.
1248::
1240::
1217:.
1213::
1205::
1182:.
1152:.
1148::
1140::
1134:3
1117:.
1113::
1105::
1099:5
1082:.
1078::
1070::
1064:2
1047:.
1043::
1035::
1029:5
1012:.
1008::
1000::
977:.
973::
965::
942:.
938::
930::
907:.
903::
895::
872:.
868::
860::
837:.
833::
825::
819:3
802:.
798::
790::
767:.
763::
755::
728:.
724::
716::
693:.
689::
681::
658:.
654::
646::
623:.
605:.
580:.
148:(
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
46:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
