566:
431:. There is a fundamental difference, though: whereas in all doubly special relativity models the Lorentz symmetry is violated, in de Sitter relativity it remains as a physical symmetry. A drawback of the usual doubly special relativity models is that they are valid only at the energy scales where ordinary special relativity is supposed to break down, giving rise to a patchwork relativity. On the other hand, de Sitter relativity is found to be invariant under a simultaneous re-scaling of
74:, but under the symmetry group of de Sitter space instead. With this assumption, empty space automatically has de Sitter symmetry, and what would normally be called the cosmological constant in general relativity becomes a fundamental dimensional parameter describing the symmetry structure of spacetime.
400:
When a cosmological constant is viewed as a kinematic parameter, the definitions of energy and momentum must be changed from those of special relativity. These changes could significantly modify the physics of the early universe if the cosmological constant was greater back then. Some speculate that
392:
In de Sitter relativity, the cosmological constant is no longer a free parameter of the same type; it is determined by the de Sitter radius, a fundamental quantity that determines the commutation relation of translation with rotations/boosts. This means that the theory of de Sitter relativity might
241:
In the pancake world, this would manifest if the creatures were living on an enormous sphere rather than on a plane. In this case, when they wander around their sphere, they would eventually come to realize that translations are not entirely separate from rotations, because if they move around on
225:
The symmetry group of special relativity is not entirely simple, due to translations. The
Lorentz group is the set of the transformations that keep the origin fixed, but translations are not included. The full Poincaré group is the semi-direct product of translations with the Lorentz group. If
388:
to the
Poincaré group for short-distance kinematics, when the magnitudes of all translations considered are very small compared to the de Sitter radius. In quantum mechanics, short distances are probed by high energies, so that for energies above a very small value related to the cosmological
534:
R. Aldrovandi, J.P. BeltrĂĄn
Almeida and J.G. Pereira have used the terms "de Sitter special relativity" and "de Sitter relativity" starting from their 2007 paper "de Sitter special relativity". This paper was based on previous work on amongst other things: the consequences of a non-vanishing
183:
The rotations around the horizontal axes would tilt objects by an infinitesimal amount. The tilt in the xâz plane (the "x-tilt") would be one parameter, and the tilt in the yâz plane (the "y-tilt") another. The symmetry group of this pancake world is then SO(2) semidirect product with
484:
While it looks as though this might pick out a preferred point in spaceâthe center of repulsion, it is more subtly isotropic. Moving to the uniformly accelerated frame of reference of an observer at another point, all accelerations appear to have a repulsion center at the new point.
180:, being the known rotations in the horizontal (xây) plane. Later on, they might discover rotations around the x- and y-axesâand in their everyday experience such rotations might always be by an infinitesimal angle, so that these rotations would effectively commute with each other.
250:
on the sphere. If the universe is the same everywhere (homogeneous) and there are no preferred directions (isotropic), then there are not many options for the symmetry group: they either live on a flat plane, or on a sphere with a constant positive curvature, or on a
215:, approaches 0. The Lorentz group is analogousâit is a simple group that turns into the Galilean group when the time range is made long compared to the space range, or where velocities may be regarded as infinitesimal, or equivalently, may be regarded as the limit
541:
Papers by other authors include: dSR and the fine structure constant; dSR and dark energy; dSR Hamiltonian
Formalism; and De Sitter Thermodynamics from Diamonds's Temperature, Triply special relativity from six dimensions, Deformed General Relativity and
171:
An analogous thing can be made to happen with the ordinary rotation group in three dimensions. If you imagine a nearly flat world, one in which pancake-like creatures wander around on a pancake flat world, their conventional unit of height might be the
295:
Modern proponents of this idea, such as S. Cacciatori, V. Gorini and A. Kamenshchik, have reinterpreted this theory as physics, not just mathematics. They postulate that the acceleration of the expansion of the universe is not entirely due to
488:
What this means is that in a spacetime with non-vanishing curvature, gravity is modified from
Newtonian gravity. At distances comparable to the radius of the space, objects feel an additional linear repulsion from the center of coordinates.
476:
contracts to the NewtonâHooke group. This has the effect that in the nonrelativistic limit, objects in de Sitter space have an extra "repulsion" from the origin: objects have a tendency to move away from the center with an outward pointing
397:. Unfortunately, the de Sitter radius, which determines the cosmological constant, is an adjustable parameter in de Sitter relativity, so the theory requires a separate condition to determine its value in relation to the measurement scale.
176:(ÎŒm), since that is how high typical structures are in their world, while their unit of distance could be the metre, because that is their body's horizontal extent. Such creatures would describe the basic symmetry of their world as
255:
with constant negative curvature. If they are not living on the plane, they can describe positions using dimensionless angles, the same parameters that describe rotations, so that translations and rotations are nominally unified.
188:, meaning that a two-dimensional rotation plus two extra parameters, the x-tilt and the y-tilt. The reason it is a semidirect product is that, when you rotate, the x-tilt and the y-tilt rotate into each other, since they form a
278:
De Sitter special relativity postulates that the empty space has de Sitter symmetry as a fundamental law of nature. This means that spacetime is slightly curved even in the absence of matter or energy. This residual
196:. In this world, the difference in height between two objects at the same x, y would be a rotationally invariant quantity unrelated to length and width. The z-coordinate is effectively separate from x and y.
203:. Then they would understand that z is really the same as x and y, since they can be mixed up by rotations. The SO(2) semidirect product R limit would be understood as the limit that the free parameter
2521:
Aldrovandi; Beltran
Almeida; Mayor; Pereira; Adenier, Guillaume; Khrennikov, Andrei Yu.; Lahti, Pekka; Man'Ko, Vladimir I.; Nieuwenhuizen, Theo M. (2007). "de Sitter Relativity and Quantum Physics".
168:. This means that the Lorentz group mixes up space and time such that they cannot be disentangled, while the Galilean group treats time as a parameter with different units of measurement than space.
292:
to be determined by observation. Due to the small magnitude of the constant, special relativity with its
Poincaré group is indistinguishable from de Sitter space for most practical purposes.
1640:
F. G. Gursey, "Introduction to the de Sitter group", Group
Theoretical Concepts and Methods in Elementary Particle Physics edited by F. G. Gursey (Gordon and Breach, New York, 1965)
267:, the only option is that spacetime has a uniform scalar curvature. If the curvature is positive, the analog of the sphere case for the two-dimensional creatures, the spacetime is
443:, and is consequently valid at all energy scales. A relationship between doubly special relativity, de Sitter space and general relativity is described by Derek Wise. See also
93:
popularized it as a hypothetical road by which mathematicians could have guessed part of the structure of general relativity before it was discovered. The discovery of the
332:
2317:
U. Moschella (2006), "The de Sitter and anti-de Sitter sightseeing tour", in
Einstein, 1905â2005 (T. Damour, O. Darrigol, B. Duplantier, and V. Rivesseau, eds.),
118:
suggested that spacetime curvature might not be due solely to gravity but he did not give any mathematical details of how this could be accomplished. In 1968
1253:
Licata, Ignazio; Leonardo
Chiatti (2009). "The archaic universe: Big Bang, cosmological term, and the quantum origin of time in projective cosmology".
427:
Since the de Sitter group naturally incorporates an invariant length parameter, de Sitter relativity can be interpreted as an example of the so-called
535:
cosmological constant, on doubly special relativity and on the NewtonâHooke group and early work formulating special relativity with a de Sitter space
584:
2220:
J. Bros; H. Epstein; U. Moschella (1998). "Analyticity properties and thermal effects for general quantum field theory on de Sitter spaceâtime".
1588:
Yu Tian; Han-Ying Guo; Chao-Guang Huang; Zhan Xu; Bin Zhou (2005). "Mechanics and NewtonâCartan-Like Gravity on the NewtonâHooke Spaceâtime".
1200:
Yu Tian; Han-Ying Guo; Chao-Guang Huang; Zhan Xu; Bin Zhou (2004). "Mechanics and NewtonâCartan-Like Gravity on the NewtonâHooke Spaceâtime".
565:
527:
In 1973 Eliano Pessa described how FantappiĂ©âArcidiacono projective relativity relates to earlier conceptions of projective relativity and to
946:
Aldrovandi, R.; BeltrĂĄn Almeida, J. P.; Pereira, J. G. (2007). "Some Implications of the Cosmological Constant to Fundamental Physics".
97:
has led to a revival of interest in de Sitter invariant theories, in conjunction with other speculative proposals for new physics, like
2604:
2585:
2151:
2089:
Han-Ying Guo; Chao-Guang Huang; Yu Tian; Zhan Xu; Bin Zhou (2007). "Snyder's Quantized Spaceâtime and De Sitter Special Relativity".
1743:
2459:
S Cacciatori; V Gorini; A Kamenshchik; U Moschella (2008). "Conservation laws and scattering for de Sitter classical particles".
369:, meaning that when all velocities are small the Poincaré group "morphs" into the Galilean group. (This can be made precise with
409:
with a large cosmological constant for a short period of time, and this might eventually be tested in the existing or planned
1856:
Mu-Lin Yan; Neng-Chao Xiao; Wei Huang; Si Li (2007). "Hamiltonian Formalism of the de-Sitter Invariant Special Relativity".
444:
66:
The idea of de Sitter invariant relativity is to require that the laws of physics are not fundamentally invariant under the
1007:
R. Aldrovandi; J.P. Beltran Almeida; C.S.O. Mayor; J.G. Pereira (2007). "Lorentz Transformations in de Sitter Relativity".
2648:
2633:
2628:
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36:
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In 2008 S. Cacciatori, V. Gorini and A. Kamenshchik published a paper about the kinematics of de Sitter relativity.
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123:
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56:
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Eventually, experiments at large angles would convince the creatures that the symmetry of the world is
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1834:
1460:
1407:
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804:
561:
366:
173:
156:. This is called a unification of space and time because the Lorentz group is
1777:
1308:"An extension of the concept of inertial frame and of Lorentz transformation"
389:
constant, the Poincaré group is a good approximation to the de Sitter group.
401:
a high energy experiment could modify the local structure of spacetime from
301:
264:
115:
32:
1351:
1332:
871:
748:
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852:
554:
Early work on formulating a quantum theory in a de Sitter space includes:
81:
in 1954, the theory remained obscure until it was rediscovered in 1968 by
1760:
551:
There are quantized or quantum versions of de Sitter special relativity.
440:
339:
243:
226:
translations are to be similar to elements of the Lorentz group, then as
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Yu Tian (2005). "De Sitter Thermodynamics from Diamonds's Temperature".
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Special relativity formed using the SO(4,1) symmetry group
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NewtonâHooke: de Sitter special relativity in the limit
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1026:
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334:to change with time, so that
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43:. In the standard theory of
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1567:10.1088/0264-9381/20/23/016
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445:MacDowellâMansouri action
429:doubly special relativity
423:Doubly special relativity
417:Doubly special relativity
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2191:1996RvMaP...8..327B
2113:2007FrPhC...2..358G
2060:2006PhRvD..73l4029D
2007:2009CQGra..26m5005G
1933:2005JHEP...06..045T
1880:2007CoTPh..48...27Y
1827:2008FoPh...38..216B
1770:2008ChPhC..32..612C
1713:2003CQGra..20.4799K
1691:Class. Quantum Grav
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1612:2005PhRvD..71d4030T
1559:2003CQGra..20.5225G
1537:Class. Quantum Grav
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1453:2004IJMPD..13.2241A
1400:2009GrCo...15..287A
1324:1976PNAS...73.1418K
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1108:2010CQGra..27o5010W
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917:2002PhLB..538..239M
844:1953PNAS...39..510I
797:2009FoPh...39....1A
741:2008AnP...520..728C
693:1968JMP.....9.1605B
620:Bull. Am. Math. Soc
529:Kaluza Klein theory
283:implies a positive
162:semi-direct product
150:Newtonian mechanics
51:, which requires a
2634:Physical cosmology
2629:General relativity
2624:Special relativity
2599:. Hadronic Press.
2222:Commun. Math. Phys
2091:Front. Phys. China
719:Annalen der Physik
395:cosmic coincidence
324:
248:parallel transport
142:special relativity
77:First proposed by
72:special relativity
45:general relativity
2553:10.1063/1.2827302
2353:10.1063/1.2752488
2305:10.1577/T07-141.1
1748:Chinese Physics C
1697:(22): 4799â4816.
1437:(10): 2241â2248.
1202:Physical Review D
978:10.1063/1.2752487
725:(9â10): 728â768.
701:10.1063/1.1664490
411:particle collider
379:group contraction
365:for low-velocity
253:Lobachevski plane
164:of rotations and
39:SO(4,1), that of
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2517:
2515:
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2374:(6): 1603â1621.
2368:Int J Theor Phys
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2315:
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1980:
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1906:
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1793:
1788:. Archived from
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1761:astro-ph/0703110
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1490:(1â4): 255â263.
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1261:(4): 1003â1018.
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1128:
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1101:
1081:
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1039:(6): 1385â1404.
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1016:
1004:
998:
997:
963:
943:
937:
936:
910:
901:(3â4): 239â245.
892:
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676:
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574:
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479:fictitious force
471:
462:In the limit as
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331:
330:
325:
291:
221:
126:showed that the
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2639:Quantum gravity
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2406:Further reading
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2169:Rev. Math. Phys
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1924:gr-qc/0504040v3
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500:Luigi FantappiĂš
495:
474:de Sitter group
463:
460:
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419:
407:de Sitter space
403:Minkowski space
352:
344:quantum gravity
316:
315:
287:
269:de Sitter space
232:non-commutative
216:
166:Galilean boosts
128:de Sitter group
113:
111:de Sitter space
107:
79:Luigi FantappiĂš
49:vacuum solution
41:de Sitter space
17:
12:
11:
5:
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2288:hep-th/0612184
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2228:(3): 535â570.
2212:
2175:(3): 327â392.
2159:
2153:978-0521233859
2152:
2134:
2104:hep-th/0607016
2097:(3): 358â363.
2081:
2044:(12): 124029.
2028:
1991:(13): 135005.
1975:
1954:
1901:
1871:hep-th/0512319
1848:
1811:(3): 216â227.
1795:
1792:on 2011-07-07.
1754:(8): 612â616.
1734:
1704:hep-th/0304101
1681:
1642:
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1603:hep-th/0411004
1580:
1550:hep-th/0308200
1527:
1497:hep-th/0012238
1474:
1421:
1384:(4): 287â294.
1368:
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1318:(5): 1418â21.
1298:
1245:
1215:hep-th/0411004
1192:
1170:10.1.1.339.919
1145:(2): 495â506.
1129:
1092:(15): 155010.
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908:hep-th/0203150
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818:
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626:(5): 635â652.
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572:Physics portal
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421:Main article:
418:
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377:'s concept of
363:Galilean group
356:Poincaré group
351:
348:
323:
309:Poincaré group
273:Poincaré group
146:Galilean group
109:Main article:
106:
103:
68:Poincaré group
59:of a constant
29:symmetry group
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1656:Nucl. Phys. B
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1484:Phys. Lett. B
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895:Phys. Lett. B
881:
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838:(6): 510â24.
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621:
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609:Freeman Dyson
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522:Freeman Dyson
519:
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298:vacuum energy
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154:Lorentz group
151:
147:
144:replaces the
143:
139:
135:
133:
132:Freeman Dyson
129:
125:
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91:Freeman Dyson
88:
84:
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69:
64:
62:
58:
57:stressâenergy
54:
50:
46:
42:
38:
34:
30:
26:
22:
2654:Group theory
2596:
2580:. Springer.
2577:
2526:
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2464:
2460:
2417:
2413:
2371:
2367:
2361:
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2168:
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2143:
2137:
2094:
2090:
2084:
2041:
2038:Phys. Rev. D
2037:
2031:
1988:
1984:
1978:
1957:
1914:
1910:
1904:
1864:(1): 27â36.
1861:
1857:
1851:
1808:
1804:
1798:
1790:the original
1751:
1747:
1737:
1694:
1690:
1684:
1662:(1): 76â96.
1659:
1655:
1645:
1636:
1593:
1590:Phys. Rev. D
1589:
1583:
1543:(23): 5225.
1540:
1536:
1530:
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1483:
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1434:
1430:
1424:
1381:
1377:
1371:
1360:
1315:
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1301:
1258:
1254:
1248:
1208:(4): 44030.
1205:
1201:
1195:
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1138:
1132:
1089:
1085:
1079:
1036:
1032:
1002:
951:
947:
941:
898:
894:
880:
835:
831:
821:
778:
774:
722:
718:
687:(10): 1605.
684:
680:
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656:
650:
623:
619:
553:
550:
487:
483:
468:
464:
461:
456:
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313:
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288:
277:
258:
240:
236:translations
224:
217:
212:
208:
204:
198:
192:and not two
185:
182:
170:
136:
114:
105:Introduction
76:
65:
63:to sustain.
61:scalar field
24:
18:
2561:11449/70009
2529:: 175â184.
2339:: 396â411.
2281:(6): 1879.
986:11449/69891
954:: 381â395.
781:(2): 1â19.
511:Henri Bacry
350:High energy
261:homogeneous
120:Henri Bacry
89:. In 1972,
83:Henri Bacry
2644:Kinematics
2618:Categories
1917:(6): 045.
663:: 229â243.
591:References
367:kinematics
174:micrometre
2536:0710.0610
2513:0909.1074
2499:118544579
2474:0710.0315
2427:0805.2584
2396:121015516
2129:119368124
2023:119296100
1998:0902.2001
1969:0807.2186
1949:119399508
1896:250880550
1786:143773103
1628:119378100
1522:119447462
1469:118889785
1391:0812.3438
1293:119262177
1268:0808.1339
1240:119378100
1165:CiteSeerX
1014:0709.3947
788:0711.2274
757:119191753
732:0807.3009
386:contracts
359:contracts
336:inflation
322:Λ
302:de Sitter
281:curvature
265:isotropic
152:with the
138:Minkowski
116:De Sitter
33:spacetime
2452:14403086
2207:17974712
2076:30161988
1843:16361512
1729:16875852
1575:26557629
1416:18473868
1352:16592318
1187:16691405
1124:16706599
1071:11703342
994:16631274
933:13986319
872:16589298
813:15298756
611:(1972).
558:See also
542:Torsion.
520:In 1972
509:In 1968
441:momentum
340:Big Bang
244:holonomy
2569:1178656
2541:Bibcode
2479:Bibcode
2432:Bibcode
2376:Bibcode
2341:Bibcode
2293:Bibcode
2260:2027732
2240:Bibcode
2187:Bibcode
2109:Bibcode
2056:Bibcode
2003:Bibcode
1929:Bibcode
1876:Bibcode
1823:Bibcode
1766:Bibcode
1709:Bibcode
1664:Bibcode
1608:Bibcode
1555:Bibcode
1502:Bibcode
1449:Bibcode
1396:Bibcode
1320:Bibcode
1273:Bibcode
1220:Bibcode
1157:Bibcode
1104:Bibcode
1051:Bibcode
966:Bibcode
913:Bibcode
863:1063815
840:Bibcode
793:Bibcode
737:Bibcode
689:Bibcode
642:0522147
361:to the
194:scalars
55:or the
35:is the
2603:
2584:
2567:
2497:
2450:
2394:
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2205:
2150:
2127:
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2021:
1947:
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1343:430307
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1185:
1167:
1122:
1069:
992:
931:
870:
860:
811:
755:
640:
472:, the
437:energy
375:Wigner
228:boosts
190:vector
158:simple
2565:S2CID
2531:arXiv
2508:arXiv
2495:S2CID
2469:arXiv
2448:S2CID
2422:arXiv
2392:S2CID
2283:arXiv
2256:S2CID
2230:arXiv
2203:S2CID
2177:arXiv
2125:S2CID
2099:arXiv
2072:S2CID
2046:arXiv
2019:S2CID
1993:arXiv
1964:arXiv
1945:S2CID
1919:arXiv
1892:S2CID
1866:arXiv
1839:S2CID
1813:arXiv
1782:S2CID
1756:arXiv
1725:S2CID
1699:arXiv
1624:S2CID
1598:arXiv
1571:S2CID
1545:arXiv
1518:S2CID
1492:arXiv
1465:S2CID
1439:arXiv
1412:S2CID
1386:arXiv
1289:S2CID
1263:arXiv
1236:S2CID
1210:arXiv
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