Coherent States of Accelerated Relativistic Quantum Particles, Vacuum Radiation and the Spontaneous Breakdown of the Conformal SU(2,2) Symmetry

TL;DR

This paper models accelerated relativistic particles using conformal group coherent states, revealing a non-linear acceleration-temperature relation and showing how accelerations induce vacuum radiation and symmetry breaking.

Contribution

It introduces a quantum description of accelerated particles via conformal group coherent states, deriving a new acceleration-temperature relation and analyzing vacuum radiation and symmetry breakdown.

Findings

Derived a non-linear relation between acceleration and temperature.

Calculated the occupation number distribution and thermodynamic properties of the accelerated state.

Showed that accelerations cause vacuum instability and radiation, breaking conformal symmetry.

Abstract

We give a quantum mechanical description of accelerated relativistic particles in the framework of Coherent States (CS) of the (3+1)-dimensional conformal group SU(2,2), with the role of accelerations played by special conformal transformations and with the role of (proper) time translations played by dilations. The accelerated ground state $\tilde\phi_0$ of first quantization is a CS of the conformal group. We compute the distribution function giving the occupation number of each energy level in $\tilde\phi_0$ and, with it, the partition function Z, mean energy E and entropy S, which resemble that of an "Einstein Solid". An effective temperature T can be assigned to this "accelerated ensemble" through the thermodynamic expression dE/dS, which leads to a (non linear) 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 Poincar\'e-invariant degenerated \theta-vacua (namely, coherent states of conformal zero modes). Special conformal transformations (accelerations) destabilize the Poincar\'e vacuum and make it to radiate.