Abstract
We analyze in detail the structure of anomalies obtained by the Fujikawa method, without using perturbative calculations. We derive most of the known results concerning consistent and covariant anomalies by using the algebraic relations of differential operators and Gaussian factors in the functional space. It turns out that this method is also useful for obtaining a simple expression of the local counterterm for the parity-conserving part of gauge anomalies which cannot be derived by the topological method. We also discuss a regulator ambiguity and obtain a general form of anomaly, which includes consistent and covariant forms, and show that different forms are shifted to one another by the redefinition of the gauge current or the energy-momentum tensor. We specify the gravitational consistent forms of anomaly in the Fujikawa method by using these results.
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