New Formulation of Anomaly,Anomaly Formula and Graphical Representation

Details New Formulation of Anomaly,Anomaly Formula and Graphical Representation New Formulation of Anomaly,Anomaly Formula and Graphical Representation

1995-09-14

arxiv.org/abs/hep-th/9509073v1

Phys.Rev. D53 (1996) 5932-5951

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, Figures are not included

Scientific paper

10.1103/PhysRevD.53.5932

A general approach to anomaly in quantum field theory is newly formulated by use of the propagator theory in solving the heat-kernel equation. We regard the heat-kernel as a sort of the point-splitting regularization in the space(-time) manifold. Fujikawa's general standpoint that the anomalies come from the path-integral measure is taken. We obtain some useful formulae which are valid for general anomaly calculation. They turn out to be the same as the 1-loop counter-term formulae except some important total derivative terms. Various anomalies in 2 and 4 dimensional theories are systematically calculated. Some important relations between them are concretely shown. As for the representation of general (global SO(n)) tensors, we introduce a graphical one. It makes the tensor structure of invariants very transparent and makes the tensor calculation so simple.

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