Derivation of a Generalized Stochastic Path-Integral Formulation Based on Ito Chalculus

A generalized path-integral formulation of stochastic quantization is given based on an Ito-type discretized Langevin equation. In the derivation, we do not have to evaluate an ill-defined factor such as a value of the step function at the singular point. The generalized path-integral formulation includes a real parameter b. The conventional two kinds of stochastic path-integral formulations, whose mutual relation has not been clear so far, are realized by choosing b=0 and b=1/2, respectively. We also establish a well-defined calculation rule which should be adopted in perturbative calculation for any value of b. The implications of this calculation rule are investigated within the framework of a lattice theory. Finally, we numerically investigate what kind of effects discretization of a stochastic action make on calculated expectation values.