Functional Determinants in Higher Derivative Lagrangian Theories

TL;DR

This paper analyzes the Euclidean path integral of the Pais-Uhlenbeck oscillator, a higher derivative gravity model, providing a detailed derivation of its propagator using Forman's theorem to understand its quantum behavior.

Contribution

It offers a pedagogical derivation of the propagator for a higher derivative Lagrangian using Forman's theorem, enhancing understanding of such theories in quantum gravity contexts.

Findings

Derivation of the propagator for the Pais-Uhlenbeck oscillator

Application of Forman's theorem to higher derivative theories

Insights into Euclidean path integrals in gravity models

Abstract

Motivated by the considerable success of alternative theories of gravity, we consider the toy model of a higher derivative Lagrangian theory, namely the Pais-Uhlenbeck oscillator studied in a recent paper by Hawking-Hertog. Its Euclidean Path Integral is studied with a certain detail and a pedagogical derivation of the propagator, which makes use of a Theorem due to Forman, is consequently proposed