Communications in Mathematical Physics

, Volume 18, Issue 4, pp 275–290 | Cite as

On the validity of ward identities

  • P. Stichel
Article

Abstract

Ward identities for matrix elements of covariant two-point time-ordered operators in the presence of an arbitrary number of subtractions are investigated. Neither the existence of naiveT-products nor the existence of equal-time commutators between current densities will be assumed. It is shown by means of the Jost-Lehmann-Dyson representation thatT*-products can always be defined such that normal Ward identities with respect to one current are valid. The simultaneous validity of normal Ward identities with respect to two currents requires a relation between equal-time charge-current commutators.

Our results show that the usual realization of current algebra in the form of Ward identities is possible even if subtractions are necessary. Some examples are discussed in detail.

Keywords

Neural Network Statistical Physic Matrix Element Complex System Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • P. Stichel
    • 1
    • 2
  1. 1.II. Institut für Theoretische Physik der Universität HamburgGermany
  2. 2.Deutsches Elektronen-Synchrotron DESYHamburg

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