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

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

2010-12-21

arxiv.org/abs/1012.4758v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, LaTeX, 3 figures. Additional information (resulting in four extra pages) and a slight change of focus has been intro

Scientific paper

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.

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