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Current commutation relations in the framework of general quantum field theory

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Abstract

In this paper we give a rigorous formulation of Gell-Mann's equal time commutation relations in the framework of general quantum field theory. We show that this can be achieved despite the nonexistence of charge operators for nonconserved currents. Starting from the properly formulated equal time commutation relations of “generalized charges”, we justify the application of the Gauss-Theorem and we discuss the limits for large times of time dependent “generalized charges”. The Jost-Lehmann-Dyson representation is used in order to show that the equal time commutation relations always lead to exactly one, frame independent, sum rule. We discuss the connection between properties of the Jost-Lehmann-Dyson spectral function and the convergence of Adler-Weisberger type sum rules.

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Authors and Affiliations

  1. II. Institut für theoretische Physik der Universität Hamburg, Germany

    B. Schroer

  2. Physikalisches Staatsinstitut der Universität Hamburg and Deutsches Elektronen-Synchroton (DESY), Hamburg

    P. Stichel

Authors
  1. B. Schroer
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  2. P. Stichel
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On leave of absence from University of Pittsburgh, Pittsburgh 13 Penna.

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Schroer, B., Stichel, P. Current commutation relations in the framework of general quantum field theory. Commun.Math. Phys. 3, 258–281 (1966). https://doi.org/10.1007/BF01649524

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  • DOI: https://doi.org/10.1007/BF01649524

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