A Consistent Path Integral Approach to Higher Derivative Oscillators

TL;DR

This paper develops a consistent path integral formulation for higher derivative oscillators, specifically the Pais-Uhlenbeck model, highlighting the role of auxiliary fields and improved UV behavior in the quantum theory.

Contribution

It introduces a novel path integral approach that incorporates canonical coordinates with auxiliary fields for higher derivative quantum oscillators.

Findings

Canonical quantization and Fock space construction for the Pais-Uhlenbeck oscillator.

Identification of a Lagrange multiplier as a necessary auxiliary field.

Enhanced ultraviolet convergence of Green functions with interactions.

Abstract

In this work, we study the Quantum Field Theory version of the higher derivative Pais-Uhlenbeck oscillator. We quantize canonically this system and construct its Fock space, as well as study its path integral. We demonstrate that the inclusion of canonical coordinates in the path integral necessarily introduces a new field, a Lagrange multiplier, which is essential for the consistent application of these coordinates in the canonical quantization framework. Finally, we analyze the improved ultraviolet convergence of the Green functions that this theory exhibits in the presence of an interaction.