Coherent states of accelerated relativistic quantum particles, vacuum radiation and the spontaneous breakdown of the conformal SU(2,2) symmetry

Abstract

ABSTRACTWe give a quantum mechanical description of accelerated relativistic particles in the framework of coherent states (CSs) of the (3+1)-dimensional conformal group SU(2, 2), with the role of accelerations and ‘kinematical redshift’ played by special conformal transformations (SCTs) and with the role of (proper) time translations played by dilations. The accelerated ground state of first quantization is a CS of the conformal group. We compute the distribution function giving the occupation number of each energy level in and, with it, the partition function , mean energy and entropy , which resemble that of an ‘Einstein solid’. An effective temperature can be assigned to this ‘accelerated ensemble’ through the thermodynamic expression , which leads to a (nonlinear) relation between acceleration and temperature different from Unruh’s (linear) formula. Then we construct the corresponding conformal-SU(2, 2)-invariant second-quantized theory and its spontaneous breakdown when selecting Poincaré-invariant degenerated θ-vacua (namely, CSs of conformal zero modes). SCTs (accelerations) destabilize the Poincaré vacuum and make it radiate.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.