Abstract
We investigate the origin of the trace (conformal) anomaly in the context of stochastic quantization. Based on the Langevin equation, we study the local Ward-Takahashi identities corresponding to the Weyl invariance and the general coordinate invariance. It is shown that the Ito's stochastic calculus essentially picks up the non-trivial Jacobian factor which appears in the path-integral measure. We also provide how to construct the Langevin equation which maintains the general coordinate invariance in consistent with the Ito's calculus.
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