Schroedinger Equation in Rotating Frame by using Stochastic Variational Method

TL;DR

This paper introduces the stochastic variational method to quantize a non-inertial particle system, illustrating how fictitious forces resemble gauge fields and discussing observable operators via stochastic Noether theorem.

Contribution

It provides a pedagogical framework for applying the stochastic variational method to non-inertial systems, linking fictitious forces to gauge-like fields and defining observables through stochastic symmetries.

Findings

Fictitious forces are represented as vector fields similar to gauge fields.

Observable operators can be derived using stochastic Noether theorem.

The method offers a new perspective on quantizing non-inertial systems.

Abstract

We give a pedagogical introduction of the stochastic variational method by considering the quantization of a non-inertial particle system. We show that the effects of fictitious forces are represented in the forms of vector fields which behave analogous to the gauge fields in the electromagnetic interaction. We further discuss that the operator expressions for observables can be defined by applying the stochastic Noether theorem.