44:
198:
106:
In a physical context, scalar fields are required to be independent of the choice of reference frame. That is, any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or
259:
293:
using the same units must agree on the numerical value of a scalar field at any given point of physical space. Scalar fields are contrasted with other physical quantities such as
204:
202:
199:
203:
279:
289:
associated with it. In this context, a scalar field should also be independent of the coordinate system used to describe the physical system—that is, any two
201:
390:
is associated with spin-0 particles. The scalar field may be real or complex valued. Complex scalar fields represent charged particles. These include the
1067:
200:
186:
of order zero, and the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field,
1072:
1062:
445:
136:
473:
Scalar fields like the Higgs field can be found within scalar–tensor theories, using as scalar field the Higgs field of the
281:
increases. Red represents positive values, purple represents negative values, and sky blue represents values close to zero.
681:
657:
430:
290:
47:
A scalar field such as temperature or pressure, where intensity of the field is represented by different hues of colors.
676:
652:
179:
403:
151:
698:, which fail to be invariant under spatial inversion, but are otherwise invariant under Lorentz transformations.
451:
563:
559:
459:
454:
represent the gravitational interaction through both a tensor and a scalar. Such attempts are for example the
492:
fields, breaking the conformal symmetry of the string, though balancing the quantum anomalies of this tensor.
211:
342:
147:
30:
This article is about associating a scalar value with every point in a space. For the set whose members are
463:
610:
571:
64:
836:
Dehnen, H.; Frommert, H.; Ghaboussi, F. (1992). "Higgs field and a new scalar–tensor theory of gravity".
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533:
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496:
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937:
888:
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810:
775:
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286:
143:
88:
76:
31:
495:
Scalar fields are hypothesized to have caused the high accelerated expansion of the early universe (
600:
511:. Massive (i.e. short-ranged) scalar fields are proposed, too, using for example Higgs-like fields.
175:
124:
100:
80:
35:
671:
1039:
1005:
927:
904:
861:
695:
551:
478:
426:
346:
1031:
525:
191:
174:, and it is typical in mathematics to impose further conditions on the field, such that it be
264:
1023:
976:
896:
853:
818:
783:
729:
647:
322:
298:
96:
72:
766:
Brans, C.; Dicke, R. (1961). "Mach's
Principle and a Relativistic Theory of Gravitation".
555:
500:
434:
167:
163:
111:) regardless of their respective points of origin. Examples used in physics include the
1019:
996:
Cervantes-Cota, J. L.; Dehnen, H. (1995). "Induced gravity inflation in the SU(5) GUT".
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422:
410:
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350:
187:
84:
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908:
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587:
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of cosmology. Massless (i.e. long-ranged) scalar fields in this context are known as
387:
92:
1043:
879:
Dehnen, H.; Frommmert, H. (1991). "Higgs-field gravity within the standard model".
605:
543:
529:
521:
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302:
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183:
957:"Inflationary universe: A possible solution to the horizon and flatness problems"
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52:
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17:
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43:
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116:
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56:
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68:
285:
Physically, a scalar field is additionally distinguished by having
119:
distribution in a fluid, and spin-zero quantum fields, such as the
399:
326:
196:
42:
481:-like (short-ranged) with the particles that get mass through it.
537:
353:, are scalar fields which describe the more familiar forces.
448:
scalar fields are used to describe the gravitational field.
922:
Brans, C. H. (2005). "The Roots of scalar–tensor theory".
586:
scalar is also found among the massless bosonic fields in
337:
of the potential energy scalar field. Examples include:
554:
gravitation is associated with the tensor field called
503:
and giving a hypothetical reason for the non-vanishing
488:
Scalar fields are found within superstring theories as
309:. More subtly, scalar fields are often contrasted with
801:
Zee, A. (1979). "Broken-Symmetric Theory of
Gravity".
570:
gravitation plus an extra set, which is equivalent to
267:
214:
562:, spacetime is extended to five dimensions and its
710:"Broken Symmetries and the Masses of Gauge Bosons"
273:
253:
321:In physics, scalar fields often describe the
8:
694:Technically, pions are actually examples of
578:, plus an extra scalar field known as the "
477:. This field interacts gravitationally and
333:, which can be obtained as a factor of the
528:to every point in space. Some examples of
1009:
980:
931:
733:
550:to every point in space. For example, in
377:Examples in quantum theory and relativity
266:
213:
341:Potential fields, such as the Newtonian
27:Assignment of numbers to points in space
621:
301:to every point of a region, as well as
254:{\displaystyle \sin(2\pi (xy+\sigma ))}
636:. Vol. II (2nd ed.). Wiley.
425:their mass, via a combination of the
7:
135:Mathematically, a scalar field on a
566:can be separated out into ordinary
441:was first detected at CERN in 2012.
182:to some order. A scalar field is a
123:. These fields are the subject of
115:distribution throughout space, the
458:theory as a generalization of the
413:of elementary particles, a scalar
170:, or more generally a subset of a
87:. The scalar may either be a pure
25:
433:. This mechanism is known as the
446:scalar theories of gravitation
248:
245:
230:
221:
1:
431:spontaneous symmetry breaking
368:field, such as those used in
325:associated with a particular
677:Encyclopedia of Mathematics
653:Encyclopedia of Mathematics
180:continuously differentiable
1089:
1068:Scalar physical quantities
823:10.1103/PhysRevLett.42.417
735:10.1103/PhysRevLett.13.508
404:strong nuclear interaction
29:
398:, as well as the charged
564:Riemann curvature tensor
499:), helping to solve the
97:scalar physical quantity
1028:10.1103/PhysRevD.51.395
982:10.1103/PhysRevD.23.347
788:10.1103/PhysRev.124.925
755:. Braunschweig: Vieweg.
752:Schwerkraft und Weltall
708:P.W. Higgs (Oct 1964).
343:gravitational potential
274:{\displaystyle \sigma }
148:complex-valued function
1073:Functions and mappings
1063:Multivariable calculus
611:Vector-valued function
452:Scalar–tensor theories
437:. A candidate for the
282:
275:
255:
48:
576:electromagnetic field
534:electromagnetic field
516:Other kinds of fields
505:cosmological constant
423:massive vector bosons
276:
256:
207:
162:may be a set in some
67:associating a single
46:
546:, which associate a
524:, which associate a
417:is used to give the
384:quantum field theory
297:, which associate a
287:units of measurement
265:
212:
208:The scalar field of
1020:1995PhRvD..51..395C
973:1981PhRvD..23..347G
942:2005gr.qc.....6063B
893:1991IJTP...30..985D
881:Int. J. Theor. Phys
850:1992IJTP...31..109D
838:Int. J. Theor. Phys
815:1979PhRvL..42..417Z
780:1961PhRv..124..925B
749:Jordan, P. (1955).
726:1964PhRvL..13..508H
696:pseudoscalar mesons
601:Scalar field theory
572:Maxwell's equations
560:Kaluza–Klein theory
460:Kaluza–Klein theory
125:scalar field theory
89:mathematical number
901:10.1007/BF00673991
858:10.1007/BF00674344
552:general relativity
464:Brans–Dicke theory
427:Yukawa interaction
347:electric potential
329:. The force is a
283:
271:
251:
49:
955:Guth, A. (1981).
540:) in meteorology.
205:
192:differential form
16:(Redirected from
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1011:astro-ph/9412032
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323:potential energy
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887:(7): 985–998 .
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803:Phys. Rev. Lett
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714:Phys. Rev. Lett
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556:Einstein tensor
518:
501:horizon problem
435:Higgs mechanism
379:
319:
317:Uses in physics
263:
262:
261:oscillating as
210:
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168:Minkowski space
164:Euclidean space
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23:
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12:
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1004:(2): 395–404.
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967:(2): 347–356.
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809:(7): 417–421.
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758:
741:
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672:"Scalar field"
663:
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541:
536:and air flow (
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483:
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475:Standard Model
468:
467:
449:
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411:Standard Model
407:
402:mediating the
396:Standard Model
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374:
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354:
351:electrostatics
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85:physical space
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933:gr-qc/0506063
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588:string theory
585:
581:
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569:
565:
561:
557:
553:
549:
545:
544:Tensor fields
542:
539:
535:
531:
530:vector fields
527:
523:
522:Vector fields
520:
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502:
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348:
344:
340:
339:
338:
336:
332:
328:
324:
316:
314:
312:
308:
307:spinor fields
304:
303:tensor fields
300:
296:
295:vector fields
292:
288:
268:
242:
239:
236:
233:
227:
224:
218:
215:
195:
193:
189:
185:
181:
177:
173:
169:
165:
161:
158:. The region
157:
153:
149:
145:
141:
138:
130:
128:
126:
122:
118:
114:
110:
104:
102:
98:
94:
93:dimensionless
90:
86:
82:
78:
74:
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66:
62:
58:
54:
45:
41:
37:
33:
19:
18:Scalar fields
1001:
998:Phys. Rev. D
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964:
961:Phys. Rev. D
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717:
713:
703:
690:
675:
666:
651:
642:
633:
630:Apostol, Tom
624:
606:Vector boson
532:include the
388:scalar field
331:vector field
320:
311:pseudoscalar
284:
184:tensor field
159:
155:
152:distribution
139:
134:
105:
61:scalar field
60:
50:
40:
439:Higgs boson
415:Higgs field
392:Higgs field
370:meteorology
358:temperature
121:Higgs field
113:temperature
83:– possibly
53:mathematics
1057:Categories
844:(1): 109.
774:(3): 925.
617:References
176:continuous
131:Definition
909:120164928
866:121308053
768:Phys. Rev
682:EMS Press
658:EMS Press
509:inflatons
497:inflation
345:, or the
291:observers
269:σ
243:σ
228:π
219:
178:or often
109:spacetime
1044:11077875
1036:10018493
648:"Scalar"
634:Calculus
632:(1969).
595:See also
582:". (The
574:for the
462:and the
429:and the
366:pressure
362:humidity
335:gradient
313:fields.
172:manifold
117:pressure
71:to each
65:function
1016:Bibcode
969:Bibcode
938:Bibcode
889:Bibcode
846:Bibcode
811:Bibcode
776:Bibcode
722:Bibcode
684:, 2001
660:, 2001
584:dilaton
580:dilaton
490:dilaton
419:leptons
409:In the
394:of the
188:density
95:) or a
57:physics
32:scalars
1042:
1034:
907:
864:
548:tensor
526:vector
479:Yukawa
456:Jordan
299:vector
137:region
99:(with
77:region
69:number
34:, see
1040:S2CID
1006:arXiv
928:arXiv
924:arXiv
905:S2CID
862:S2CID
558:. In
400:pions
364:, or
327:force
190:, or
142:is a
101:units
81:space
75:in a
73:point
63:is a
36:field
1032:PMID
538:wind
421:and
386:, a
305:and
144:real
59:, a
55:and
1024:doi
977:doi
897:doi
854:doi
819:doi
784:doi
772:124
730:doi
444:In
382:In
349:in
216:sin
154:on
150:or
146:or
103:).
79:of
51:In
1059::
1038:.
1030:.
1022:.
1014:.
1002:51
1000:.
975:.
965:23
963:.
959:.
936:.
926:.
903:.
895:.
885:30
883:.
860:.
852:.
842:31
840:.
817:.
807:42
805:.
782:.
770:.
728:.
718:13
716:.
712:.
680:,
674:,
656:,
650:,
590:.)
360:,
356:A
194:.
166:,
127:.
1046:.
1026::
1018::
1008::
985:.
979::
971::
944:.
940::
930::
911:.
899::
891::
868:.
856::
848::
825:.
821::
813::
790:.
786::
778::
738:.
732::
724::
466:.
406:.
372:.
249:)
246:)
240:+
237:y
234:x
231:(
225:2
222:(
160:U
156:U
140:U
91:(
38:.
20:)
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