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Register a new userCoherent States of Accelerated Relativistic Quantum Particles, Vacuum Radiation and the Spontaneous Breakdown of the Conformal SU(2,2) Symmetry
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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 $tildephi_0$ of first quantization is a CS of the conformal group. We compute the distribution function giving the occupation number of each energy level in $tildephi_0$ 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 Unruhs (linear) formula. Then we construct the corresponding conformal-SU(2,2)-invariant second quantized theory and its spontaneous breakdown when selecting Poincare-invariant degenerated theta-vacua (namely, coherent states of conformal zero modes). Special conformal transformations (accelerations) destabilize the Poincare vacuum and make it to radiate.
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We revise the unireps. of $U(2,2)$ describing conformal particles with continuous mass spectrum from a many-body perspective, which shows massive conformal particles as compounds of two correlated massless particles. The statistics of the compound (boson/fermion) depends on the helicity $h$ of the massless components (integer/half-integer). Coherent states (CS) of particle-hole pairs (excitons) are also explicitly constructed as the exponential action of exciton (non-canonical) creation operators on the ground state of unpaired particles. These CS are labeled by points $Z$ ($2times 2$ complex matrices) on the Cartan-Bergman domain $mathbb D_4=U(2,2)/U(2)^2$, and constitute a generalized (matrix) version of Perelomov $U(1,1)$ coherent states labeled by points $z$ on the unit disk $mathbb D_1=U(1,1)/U(1)^2$. Firstly we follow a geometric approach to the construction of CS, orthonormal basis, $U(2,2)$ generators and their matrix elements and symbols in the reproducing kernel Hilbert space $mathcal H_lambda(mathbb D_4)$ of analytic square-integrable holomorphic functions on $mathbb D_4$, which carries a unitary irreducible representation of $U(2,2)$ with index $lambdainmathbb N$ (the conformal or scale dimension). Then we introduce a many-body representation of the previous construction through an oscillator realization of the $U(2,2)$ Lie algebra generators in terms of eight boson operators with constraints. This particle picture allows us for a physical interpretation of our abstract mathematical construction in the many-body jargon. In particular, the index $lambda$ is related to the number $2(lambda-2)$ of unpaired quanta and to the helicity $h=(lambda-2)/2$ of each massless particle forming the massive compound.
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