Berry's Phase and Euclidean Path Integral

TL;DR

This paper introduces a method to compute Berry's phase using Euclidean path integrals, demonstrating its application to generalized harmonic oscillators and spin models, with a systematic adiabatic expansion approach.

Contribution

It presents a novel Euclidean path integral-based method for calculating Berry's phase, applicable to various quantum systems including oscillators and spin models.

Findings

Method effectively captures Berry's phase via imaginary parts in the exponent.

Application to generalized harmonic oscillator shows universality in single degree systems.

Systematic adiabatic expansion method is developed for different models.

Abstract

A method for finding Berry's phase is proposed under the Euclidean path integral formalism. It is characterized by picking up the imaginary part from the resultant exponent. Discussion is made on the generalized harmonic oscillator which is shown being so universal in a single degree case. The spin model expressed by creation and annihilation operators is also discussed. A systematic way of expansion in the adiabatic approximation is presented in every example.