New Formulation of Anomaly,Anomaly Formula and Graphical Representation

Abstract

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.

42 pages, Figures are not included

References in corpus (3)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Graphical Representation of Invariants and Covariants in General Relativity

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• Weyl Anomaly in Higher Dimensions and Feynman Rules in Coordinate Space
• Temperature in Fermion Systems and the Chiral Fermion Determinant
• Graphical Classification of Global SO(n) Invariants and Independent General Invariants
• New Regularization Using Domain Wall
• Weak Field Expansion of Gravity and Graphical Representation