The Unruh effect for higher derivative field theory

TL;DR

This paper investigates the Unruh effect in a higher derivative scalar field theory modeled by the Pais-Uhlenbeck oscillator, revealing particle creation for different frequencies and no creation in the equal frequency limit, with a focus on quantum and thermal properties.

Contribution

It introduces a Hamiltonian transformation compatible with PT-symmetric quantum mechanics for the Pais-Uhlenbeck model and analyzes particle creation and thermal effects in this higher derivative context.

Findings

Particle and antiparticle creation occur for different frequencies.

No particle creation in the equal frequencies limit due to annihilation.

A Poincaré invariant two-point function is constructed for thermal analysis.

Abstract

We analyse the emergence of the Unruh effect within the context of a field Lagrangian theory associated to the Pais-Uhlenbeck fourth order oscillator model. To this end, we introduce a transformation that brings the Hamiltonian bounded from below and is consistent with $\mathcal{PT}$-symmetric quantum mechanics. We find that, as far as we consider different frequencies within the Pais-Uhlenbeck model, a particle together with an antiparticle of different masses are created as may be traced back to the Bogoliubov transformation associated to the interaction between the Unruh-DeWitt detector and the higher derivative scalar field. On the contrary, whenever we consider the equal frequencies limit, no particle creation is detected as the pair particle/antiparticle annihilate each other. Further, following Moschella and Schaeffer, we construct a Poincar\'e invariant two-point function for the Pais-Uhlenbeck model, which in turn allows us to perform the thermal analysis for any of the emanant particles.