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The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory

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Abstract

In the framework of perturbative quantum field theory a new, universal renormalization condition (called Master Ward Identity) was recently proposed by one of us (M.D.) in a joint paper with F.-M. Boas. The main aim of the present paper is to get a better understanding of the Master Ward Identity by analyzing its meaning in classical field theory. It turns out that it is the most general identity for classical local fields which follows from the field equations. It is equivalent to a generalization of the Schwinger-Dyson Equation and is closely related to the Quantum Action Principle of Lowenstein and Lam. As a byproduct we give a self-contained treatment of Peierls’ manifestly covariant definition of the Poisson bracket.

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Authors and Affiliations

  1. Institut für Theoretische Physik, 37073, Göttingen, Germany

    Michael Dütsch

  2. Institut für Theoretische Physik, 22761, Hamburg, Germany

    Klaus Fredenhagen

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  1. Michael Dütsch
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  2. Klaus Fredenhagen
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Correspondence to Michael Dütsch.

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Communicated by J.Z. Imbrie

Work supported by the Deutsche Forschungsgemeinschaft.

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Dütsch, M., Fredenhagen, K. The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory. Commun. Math. Phys. 243, 275–314 (2003). https://doi.org/10.1007/s00220-003-0968-4

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