Abstract
An anomalous gauge theory can be quantized consistently by perturbation theory instead of Dirac's method in the Hamiltonian formulation. It reveals the gradually varying commutator structures according to the higher-order vertex corrections and the series sum of the commutator algebra of each order becomes the Dirac brackets for the bosonized action. However, the perturbation approach in the Lorentz-invariant gauge does not give the Dirac brackets.
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