Abstract
We investigate a general framework of the stochastic quantization method for theories with field· dependent metrics. The differential of a field has different properties from ordinary (i.e., not stochastic) one, which enforces us to define the Langevin equation, the invariant measure and others in rather complicated forms. The Parisi·Sourlas supersymmetry in this framework is also discussed and shown to be defined in a reference frame.
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