Time-ordered operators and Feynman-Dyson algebras

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dc.contributorVirginia Techen
dc.contributor.authorGill, T. L.en
dc.contributor.authorZachary, W. W.en
dc.contributor.departmentPhysicsen
dc.date.accessed2014-03-20en
dc.date.accessioned2014-04-09T18:12:29Zen
dc.date.available2014-04-09T18:12:29Zen
dc.date.issued1987-07en
dc.description.abstractAn approach to time‐ordered operators based upon von Neumann’s infinite tensor product Hilbert spaces is used to define Feynman–Dyson algebras. This theory is used to show that a one‐to‐one correspondence exists between path integrals and semigroups, which are integral operators defined by a kernel, the reproducing property of the kernel being a consequence of the semigroup property. For path integrals constructed from two semigroups, the results are more general than those obtained by the use of the Trotter–Kato formula. Perturbation series for the Feynman–Dyson operator calculus for time evolution and scattering operators are discussed, and it is pointed out that they are ‘‘asymptotic in the sense of Poincaré’’ as defined in the theory of semigroups, thereby giving a precise formulation to a well‐known conjecture of Dyson stated many years ago in the context of quantum electrodynamics. Moreover, the series converge when these operators possess suitable holomorphy properties.en
dc.identifier.citationGill, T. L.; Zachary, W. W., "Time-ordered operators and Feynman-Dyson algebras," J. Math. Phys. 28, 1459 (1987); http://dx.doi.org/10.1063/1.527499en
dc.identifier.doihttps://doi.org/10.1063/1.527499en
dc.identifier.issn0022-2488en
dc.identifier.urihttp://hdl.handle.net/10919/47095en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/jmp/28/7/10.1063/1.527499en
dc.language.isoen_USen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectalgebrasen
dc.subjectintegrationen
dc.subjectoperator theoryen
dc.subjectcalculusen
dc.subjecthilbert spaceen
dc.subjectperturbation theoryen
dc.subjectquantum electrodynamicsen
dc.subjectscattering theoryen
dc.subjecttensor methodsen
dc.titleTime-ordered operators and Feynman-Dyson algebrasen
dc.title.serialJournal of Mathematical Physicsen
dc.typeArticle - Refereeden

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