## 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

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".…

Author: | Andreas U. Schmidt |
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URN: | urn:nbn:de:hebis:30-11324 |

Document Type: | Article |

Language: | English |

Date of Publication (online): | 2005/06/21 |

Year of first Publication: | 2002 |

Publishing Institution: | Univ.-Bibliothek Frankfurt am Main |

Release Date: | 2005/06/21 |

Tag: | Krein space; Pontrjagin space; Schwinger model; quantum field theory |

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: | Mathematik |

Dewey Decimal Classification: | 510 Mathematik |

MSC-Classification: | 81-02 Research exposition (monographs, survey articles) |

81T05 Axiomatic quantum field theory; operator algebras | |

81T10 Model quantum field theories | |

81T13 Yang-Mills and other gauge theories [See also 53C07, 58E15] | |

Sammlungen: | Universitätspublikationen |

Licence (German): | Veröffentlichungsvertrag für Publikationen |