Mathematical problems of gauge quantum field theory : a survey of the Schwinger model

  • This extended write-up of a talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge quantum field theory, I cover the following subjects: The axiomatics of quantum field theory, formulation of quantum field theory in terms of Wightman functions, reconstruction of the state space, the local formulation of gauge theories, indefiniteness of the Wightman functions in general and in the special case of the Schwinger model, the state space of the Schwinger model, special features of the model. New results are contained in the Mathematical Appendix, where I consider in an abstract setting the Pontrjagin space structure of a special class of indefinite inner product spaces - the so called quasi-positive ones. This is motivated by the indefinite inner product space structure appearing in the above context and generalizes results of Morchio and Strocchi [J. Math. Phys. 31 (1990) 1467], and Dubin and Tarski [J. Math. Phys. 7 (1966) 574]. See the corresponding paper: Schmidt, Andreas U.: "Infinite Infrared Regularization and a State Space for the Heisenberg Algebra" and the presentation "Infinite Infrared Regularization in Krein Spaces".

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Metadaten
Author:Andreas U. SchmidtGND
URN:urn:nbn:de:hebis:30-11324
ISSN:0860-0120
ISSN:0083-4386
ArXiv Id:http://arxiv.org/abs/hep-th/9707166v3
Document Type:Article
Language:English
Year of Completion:2002
Year of first Publication:2002
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2005/06/21
Tag:Krein space; Pontrjagin space; Schwinger model; quantum field theory
Page Number:22
First Page:1
Last Page:22
Note:
Aktualisierte Fassung, zuerst erschienen in: Universitatis Iagellonicae acta mathematica, 34.1997, S. 113-134
Source:Version of March 2002, Orig. publ. in Universitatis Iagellonicae Acta Mathematica Fasciculus IV (1997) 113-134, http://arxiv.org/abs/hep-th/9707166 , http://www.math.uni-frankfurt.de/~aschmidt/#eprints
HeBIS-PPN:134978560
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:81-XX QUANTUM THEORY / 81-02 Research exposition (monographs, survey articles)
81-XX QUANTUM THEORY / 81Txx Quantum field theory; related classical field theories [See also 70Sxx] / 81T05 Axiomatic quantum field theory; operator algebras
81-XX QUANTUM THEORY / 81Txx Quantum field theory; related classical field theories [See also 70Sxx] / 81T10 Model quantum field theories
81-XX QUANTUM THEORY / 81Txx Quantum field theory; related classical field theories [See also 70Sxx] / 81T13 Yang-Mills and other gauge theories [See also 53C07, 58E15]
Licence (German):License LogoDeutsches Urheberrecht