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1119:{\displaystyle j^{\mu }:={\frac {d{\mathcal {L}}}{d(\partial _{\mu })\phi }}\,{\frac {d(\delta \phi )}{d\alpha }}{\bigg |}_{\alpha =0}+{\frac {d{\mathcal {L}}}{d(\partial _{\mu })\phi ^{*}}}\,{\frac {d(\delta \phi ^{*})}{d\alpha }}{\bigg |}_{\alpha =0}=i\,\phi \,(\partial ^{\mu }\phi ^{*})-i\,\phi ^{*}\,(\partial ^{\mu }\phi )}
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Peskin, Michael E.; Schroeder, Daniel V. (1995). "Chapter I.2.2. Elements of
Classical Field Theory".
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of some quantity in the system under study. In practical terms, all conserved currents are the
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Concept in physics and mathematics that satisfies the continuity equation
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connects the existence of a conserved current to the existence of a
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the gauge fields couple to conserved currents. For example, the
1162:(2nd ed.). Reading, MA: Addison-Wesley. pp. 588–596.
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Conserved currents play an extremely important role in
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1185:(Third ed.). Prentice Hall. pp.
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167:{\displaystyle \partial _{\mu }j^{\mu }=0}
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1208:An Introduction to Quantum Field Theory
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314:Conserved quantities and symmetries
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818:\delta \phi =\phi '-\phi
365:conservation of momentum
121:{\displaystyle j^{\mu }}
32:This article includes a
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53:Please help
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59:introducing
1346:Categories
1147:References
434:divergence
404:, because
375:rotational
369:Space and
324:continuous
1111:ϕ
1106:μ
1102:∂
1092:∗
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1080:−
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787:Defining
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617:∂
557:ρ
528:ρ is the
499:⋅
496:∇
484:∂
479:ρ
476:∂
442:4-current
426:foliation
257:∫
211:∂
207:∂
154:μ
144:μ
140:∂
114:μ
1367:Symmetry
1156:(1980).
1130:See also
807:′
750:′
448:Examples
410:symmetry
361:momentum
1187:356–357
590:above.
538:is the
329:. The
291:is the
99:current
91:physics
55:improve
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524:where
438:charge
348:energy
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387:phase
357:Space
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344:Time
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