The Unruh effect for higher derivative field theory

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 $\mathcal{P}\mathcal{T}$-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 Poincaré 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.

12 pages, no figures

References in corpus (4)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Pais-Uhlenbeck Oscillator and Negative Energies
• Ostrogradski approach for the Regge-Teitelboim type cosmology
• A note on canonical quantization of fields on a manifold