Local quantum constraints

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dc.contributor.author Grundling, Hendrik
dc.contributor.author Lledó Macau, Fernando
dc.date.accessioned 2010-02-12T13:43:24Z
dc.date.available 2010-02-12T13:43:24Z
dc.date.issued 2000
dc.identifier.bibliographicCitation Reviews in Mathematical Physics, 2000, vol. 12, n. 9, p. 1159-1218
dc.identifier.issn 0129-055X (Print)
dc.identifier.issn 1793-6659 (Online)
dc.identifier.uri http://hdl.handle.net/10016/6849
dc.description 60 pages, no figures.-- MSC2000 codes: 46L60, 81T05, 81R15.
dc.description MR#: MR1794238 (2001m:81159)
dc.description Zbl#: Zbl 0991.46038
dc.description.abstract We analyze the situation of a local quantum field theory with constraints, both indexed by the same set of space-time regions. In particular we find "weak" Haag–Kastler axioms which will ensure that the final constrained theory satisfies the usual Haag–Kastler axioms. Gupta–Bleuler electromagnetism is developed in detail as an example of a theory which satisfies the "weak" Haag–Kastler axioms but not the usual ones. This analysis is done by pure C*-algebraic means without employing any indefinite metric representations, and we obtain the same physical algebra and positive energy representation for it than by the usual means. The price for avoiding the indefinite metric, is the use of nonregular representations and complex valued test functions. We also exhibit the precise connection with the usual indefinite metric representation.
dc.description.abstract We conclude the analysis by comparing the final physical algebra produced by a system of local constrainings with the one obtained from a single global constraining and also consider the issue of reduction by stages. For the usual spectral condition on the generators of the translation group, we also find a "weak" version, and show that the Gupta–Bleuler example satisfies it.
dc.description.sponsorship The authors thank the sfb 288 for support during the visit to University of Potsdam. We also benefitted from an ARC grant which funded a visit of F.Ll. to the University of New South Wales. Finally, F.Ll. would like to thank Sergio Doplicher for his kind hospitality at the ‘Dipartamento di Matematica dell’Università di Roma "La Sapienza" in March 2000, when the final version of this paper was prepared. The visit was supported by a EU TMR network "Implementation of concept and methods from Non–Commutative Geometry to Operator Algebras and its applications", contract no. ERB FMRX-CT 96-0073.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher World Scientific Publishing
dc.rights © World Scientific Publishing
dc.subject.other Quantum system with constraints
dc.subject.other Algebraic Quantum Field Theory (AQFT)
dc.subject.other Dirac state
dc.subject.other Gupta-Bleuler electromagnetism
dc.subject.other Field C*-algebra
dc.subject.other Constraint set
dc.subject.other Maximal C*-algebra of physical observables
dc.subject.other Weak Haag-Kastler axioms
dc.subject.other Local quantum constraints
dc.title Local quantum constraints
dc.type article
dc.type.review PeerReviewed
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1142/S0129055X00000459
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1142/S0129055X00000459
dc.rights.accessRights openAccess
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