Transition Amplitude within the Stochastic Quantization Scheme -- Perturbative Treatment

TL;DR

This paper demonstrates that stochastic quantization can be used to compute quantum transition amplitudes perturbatively, reproducing standard results and including higher-order effects systematically.

Contribution

It introduces a perturbative approach within stochastic quantization that reproduces known quantum amplitudes and systematically accounts for higher-order corrections.

Findings

Stochastic quantization reproduces standard quantum transition amplitudes.

Higher-order effects are systematically incorporated at the lowest order.

The method aligns with conventional results in quantum mechanics.

Abstract

The quantum mechanical transition amplitudes are calculated perturbatively on the basis of the stochastic quantization method of Parisi and Wu. It is shown that the stochastic scheme reproduces the ordinary result for the amplitude and systematically incorporates higher-order effects, even at the lowest order.