Euclidean Path Integral and Higher-Derivative Theories

TL;DR

This paper explores the Euclidean path integral formulation for higher-derivative theories, focusing on the Pais-Uhlenbeck oscillator, revealing the structure of the quantum state space and the complex classical dynamics involved.

Contribution

It provides a detailed analysis of the operator algebra and state space structure in higher-derivative quantum theories, extending the Euclidean path integral approach to field theories.

Findings

Reconstruction of operator algebra for higher-derivative theories

Identification of the state space structure in the quantum theory

Connection between classical complex dynamics and quantum quantization

Abstract

We consider the Euclidean path integral approach to higher-derivative theories proposed by Hawking and Hertog (Phys. Rev. D65 (2002), 103515). The Pais-Uhlenbeck oscillator is studied in some detail. The operator algebra is reconstructed and the structure of the space of states revealed. It is shown that the quantum theory results from quantizing the classical complex dynamics in which the original dynamics is consistently immersed. The field-theoretical counterpart of Pais-Uhlenbeck oscillator is also considered.