437:. The infinitesimal change in the amplitude is clearly given by Schwinger's formula. Conversely, starting from Schwinger's formula, it is easy to show that the fields obey canonical commutation relations and the classical equations of motion, and so have a path integral representation. Schwinger's formulation was most significant because it could treat fermionic anticommuting fields with the same formalism as bose fields, thus implicitly introducing differentiation and integration with respect to anti-commuting coordinates.
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In the path integral formulation, the transition amplitude is represented by the sum over all histories of
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where the action is a classical function, the modern formulation of the two formalisms are identical.
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239:{\displaystyle \delta \langle B|A\rangle =i\langle B|\delta S|A\rangle ,\ }
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is targeted towards quantum mechanics. The action becomes a
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Not to be confused with
Schwinger's variational principle,
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Schwinger, Julian (2001). Englert, Berthold-Georg (ed.).
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where the derivative is with respect to small changes (
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Suppose we have two states defined by the values of a
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304:{\displaystyle S=\int {\mathcal {L}}\,\mathrm {d} t}
611:"Quantum mechanics in terms of an action principle"
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95:. Although it is superficially different from the
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59:in a series of articles starting 1950.
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164:Schwinger's quantum action principle
41:Schwinger's quantum action principle
104:complete set of commuting operators
550:Schweber, Silvan S. (2005-05-31).
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55:. This theory was introduced by
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502:"The Quantum Action Principle"
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328:{\displaystyle {\mathcal {L}}}
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67:In Schwingers approach, the
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430:{\displaystyle |B\rangle }
402:{\displaystyle |A\rangle }
155:{\displaystyle |B\rangle }
127:{\displaystyle |A\rangle }
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27:Approach to quantum theory
609:Bracken, P (1997-04-04).
500:Dittrich, Walter (2021),
477:10.1007/978-3-662-04589-3
97:path integral formulation
381:representing the states
370:{\displaystyle \exp(iS)}
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262:{\displaystyle \delta }
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88:{\displaystyle S}
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453:References
339:operator.
635:0008-4204
578:0027-8424
532:236705758
425:⟩
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283:∫
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63:Approach
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206:B
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36:.
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