caa a22 4500 463195396 CHVBK 20180406164921.0 cr unu---uuuuu 170326e20070101xx s 000 0 eng 10.1007/s10773-006-9199-8 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9199-8 Regularization as Quantization in Reducible Representations of CCR [Elektronische Daten] [Marek Czachor, Jan Naudts] A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials (an alternative to the Gupta-Bleuler method) is tested on the example of quantum electromagnetic fields produced by a classical current. The Heisenberg dynamics can be consistently formulated since the fields are given by operators and not operator-valued distributions. The scheme involves a Hamiltonian whose free part is modified but the minimal-coupling interaction is the standard one. Solving Heisenberg equations of motion under the assumption that the fields are free for times t 0 = ±∞ we arrive at retarded and advanced solutions. Once we have these solutions we can deduce the form of evolution of retarded and advanced fields between two arbitrary finite times. The appropriate unitary evolution operators are found and their generators are computed. Now the generators involve the same free part as before, but the interaction term turns out to be modified. For a pointlike charge localized on a world-line z a (t) we find the interaction term of the form $$-q\vec{A}(z(t))\cdot\vec v(t)-q\int d\vec z\cdot\vec {E}$$ where the integration is along those parts of the charge world-line where the charge velocity is nonzero. There is no self-energy contribution. Next we compute photon statistics. Poisson statistics naturally results and infrared divergence can be avoided even for pointlike sources. Classical fields produced by classical sources can be obtained if one computes coherent-state averages of Heisenberg-picture operators. It is shown that the new form of representation automatically smears out pointlike currents. We discuss in detail Poincaré covariance of the theory and the role of Bogoliubov transformations for the issue of gauge invariance. The representation we employ is parametrized by a number that is related to Rényi's α. It is shown that the "Shannon limit” α→ 1 plays here a role of a correspondence principle with the standard regularized formalism. Springer Science+Business Media, Inc., 2006 quantization nationallicence guantum optics nationallicence quantum field theory nationallicence Czachor Marek Katedra Fizyki Teoretycznej i Metod Matematycznych, Politechnika Gdańska, 80-952, Gdańsk, Poland aut Naudts Jan Departement Fysica, Universiteit Antwerpen, B2610, Antwerpen, Belgium aut International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/1(2007-01-01), 70-101 0020-7748 46:1<70 2007 46 10773 https://doi.org/10.1007/s10773-006-9199-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9199-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Czachor Marek Katedra Fizyki Teoretycznej i Metod Matematycznych, Politechnika Gdańska, 80-952, Gdańsk, Poland aut NATIONALLICENCE 700 1- Naudts Jan Departement Fysica, Universiteit Antwerpen, B2610, Antwerpen, Belgium aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/1(2007-01-01), 70-101 0020-7748 46:1<70 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer