TY - JOUR
A1 - Schmidt, Andreas U.
T1 - Mathematical problems of gauge quantum field theory : a survey of the Schwinger model
N2 - 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".
KW - quantum field theory
KW - Schwinger model
KW - Krein space
KW - Pontrjagin space
Y1 - 2002
UR - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/4357
UR - https://nbn-resolving.org/urn:nbn:de:hebis:30-11324
SN - 0860-0120
SN - 0083-4386
N1 - Aktualisierte Fassung, zuerst erschienen in: Universitatis Iagellonicae acta mathematica, 34.1997, S. 113-134
SP - 1
EP - 22
ER -