Generalized Ward Identity and Unified Treatment of Conservation Laws

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Abstract
A technique for deriving conservation laws directly from field equations without recourse to the Lagrangians or Noether's theorem is reviewed and extended. The method allows a simple treatment of the so‐called ``generalized'' conservation laws including Lipkin's ``zilch.'' An interesting feature which results from our approach is the existence of conserved currents for discrete as well as continuous symmetries. It is also pointed out that conservation laws do not always follow from the invariance of equation of motion if it is not derivable from a Lagrangian. Finally, we show how our method can be applied to the normalization of wavefunctions of composite particles such as Bethe‐Salpeter wavefunctions.

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