Abstract
Minkowski stochastic quantization is applied to deJ;.ive Ward-Takahashi identities in both unbroken and spontaneously broken theories. The introduction of the fifth time in the Parisi-Wu method offers a possibility of the order parameter growing as the fictitious time evolves; it is connected with a modified Langevin equation that is capable of describing spontaneous breakdown of symmetry. The (unbroken) scalar theory is regularized in the two markovian schemes proposed so far, which coincide with each other in the external-field approximation without self-interaction. It is shown that the external-field markovian stochastic regularization is equivalent to a regularized path-integral method which dispenses with detailed definition of the measure, considering the trace anomaly as a workable example. Extension to the spinor case is also discussed.
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