Abstract

Electromagnetic fields are quantized in a manifestly covariant way by means ofa class of reducible "center-of-mass N-representations" of the algebra of canonical commutationrelations (CCR). The four-potential Aa(x) transforms in these representations as aHermitian four-vector field in Minkowski four-position space (without change of gauge), butin momentum space it splits into spin-1 massless photons and two massless scalars. Whatwe call quantum optics is the spin-1 sector of the theory. The scalar fields have physicalstatus similar to that of dark matter (spin-1 and spin-0 particle numbers are separately conserved).There are no negative-norm or zero-norm states. Unitary dynamics is given by thepoint-form interaction picture, with minimal-coupling Hamiltonian constructed from fieldsthat are free on the null-cone boundary of the Milne universe. SL(2,C) transformations aswell as the dynamics are represented unitarily in the Hilbert space corresponding to N fourdimensionaloscillators. Vacuum is a Bose-Einstein condensate of the N-oscillator gas andis given by any N-oscillator product state annihilated by all annihilation operators. The formof Aa(x) is determined by an analogue of the twistor equation. The same equation guaranteesthat the set of vacuum states is Poincaré invariant. The formalism is tested on quantumfields produced by pointlike classical sources. Photon statistics is well defined even forpointlike charges, with ultraviolet and infrared regularizations occurring automatically as aconsequence of the formalism. The probabilities are not Poissonian but of a Rényi type withα = 1 − 1/N; the Shannon limit N→∞is an ultraviolet/infrared-regularized Poisson distribution.The average number of photons occurring in Bremsstrahlung splits into two parts:The one due to acceleration, and the one that remains nonvanishing even for inertially movingcharges. Classical Maxwell electrodynamics is reconstructed from coherent-state averagedsolutions of Heisenberg equations. We show in particular that static pointlike chargespolarize vacuum and produce effective charge densities and fields whose form is sensitiveto both the choice of representation of CCR and the corresponding vacuum state.M. Czachor () · K. WrzaskKatedra Fizyki Teoretycznej i Informatyki Kwantowej, Politechnika Gda´nska, 80-952 Gda´nsk, Polande-mail: mczachor@pg.gda.plM. CzachorCentrum Leo Apostel (CLEA), Vrije Universiteit Brussel, 1050 Brussels, Belgium

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