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

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          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.

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          Author and article information

          Journal
          21 December 2010
          2011-08-10
          10.1088/1751-8113/45/24/244010
          1012.4758

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          81R30, 81R05, 42B05, 30H20, 42C15
          J. Phys. A: Math. Theor. 45 (2012) 244010
          25 pages, LaTeX, 3 figures. Additional information (resulting in four extra pages) and a slight change of focus has been introduced in order to make the line of arguments more clear. Title changed accordingly
          gr-qc hep-th math-ph math.MP

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