Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator

TL;DR

This paper analyzes the path integral formulation of pseudo-Hermitian quantum mechanics, emphasizing how the metric operator influences the generating functional, thus clarifying foundational aspects of PT-symmetric quantum theories.

Contribution

It introduces a detailed analysis of the metric operator’s role in the path integral formulation of pseudo-Hermitian quantum mechanics.

Findings

The metric operator explicitly appears in the generating functional.

Path integral formulation can be consistently extended to PT-symmetric systems.

Clarifies the mathematical structure underlying pseudo-Hermitian quantum theories.

Abstract

We provide a careful analysis of the generating functional in the path integral formulation of pseudo-Hermitian and in particular PT-symmetric quantum mechanics and show how the metric operator enters the expression for the generating functional.