Euclidean path integral of the scalar Lee-Wick model

TL;DR

This paper develops a Euclidean path integral formulation for the scalar Lee-Wick model using canonical quantization with an indefinite metric, demonstrating how to handle ghost degrees in the path integral.

Contribution

It introduces a field diagonal representation and constructs the Euclidean path integral for the Lee-Wick model, including a detailed example with the quantum mechanical case.

Findings

Path integrals can be formulated despite indefinite metric.

Integration contours for ghost degrees are along the real axis.

The method is demonstrated explicitly for the quantum mechanical Lee-Wick model.

Abstract

On the basis of the canonical quantization procedure, in which we need the indefinite metric Hilbert space, we formulate field diagonal representation for the scalar Lee-Wick model. Euclidean path integral for the model is then constructed in terms of the eigenvector of field operators. Taking the quantum mechanical Lee-Wick model as an example, we demonstrate how to formulate path integrals for such systems in detail. We show that, despite the use of indefinite metric representation, integration contours for ghost degrees can be taken along the real axis.