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A general approach to anomaly in quantum field theory is newly formulated byuse of the propagator theory in solving the heat-kernel equation. We regard theheat-kernel as a sort of the point-splitting regularization in the space(-time)manifold. Fujikawa's general standpoint that the anomalies come from thepath-integral measure is taken. We obtain some useful formulae which are validfor general anomaly calculation. They turn out to be the same as the 1-loopcounter-term formulae except some important total derivative terms. Variousanomalies in 2 and 4 dimensional theories are systematically calculated. Someimportant relations between them are concretely shown. As for therepresentation of general (global SO(n)) tensors, we introduce a graphical one.It makes the tensor structure of invariants very transparent and makes thetensor calculation so simple.Comment: 42 pages, Figures are not include

New formulation of the anomaly, the anomaly formula, and a graphical representation