Loop representation of charged particles interacting with Maxwell and Chern-Simons fields (original) (raw)
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A loop representation for the quantum Maxwell field
Quantization of the free Maxwell field in Minkowski space is carried out using a loop representation and shown to be equivalent to the standard Fock quantization. Because it is based on coherent state methods, this framework may be useful in quantum optics. It is also well-suited for the discussion of issues related to flux quantization in condensed matter physics. Our own motivation, however, came from a non-perturbative approach to quantum gravity. The concrete results obtained in this paper for the Maxwell field provide independent support for that approach. In addition, they offer some insight into the physical interpretation of the mathematical structures that play, within this approach, an essential role in the description of the quantum geometry at Planck scale.
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Classical description of a particle interacting with a non-Abelian gauge field
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2009
This work is devoted to the sudy of the vacuum structure, special relativity, electrodynamics of interacting charged point particles and quantum mechanics, and is a continuation of [6, 7]. Based on the vacuum field theory no-geometry approach, the Lagrangian and Hamiltonian reformulation of some alternative classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed for some alternative electrodynamics models. By means of the developed approach a combined description, both of electrodynamics and gravity, is analyzed. MIRAMARE – TRIESTE September 2008 nikolai bogolubov@hotmail.com pryk.anat@ua.fm, prykanat@cybergal.com
2010
The work is devoted to studying the vacuum structure, special relativity, electrodynamics of inter acting charged point particles and quantum mechanics, and is a continuation of . Based on the vacuum field theory no geometry approach, the Lagrangian and Hamiltonian reformulation of some alternative clas sical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed for some alternative electrodynamics models. Within an approach developed a possibility of the combined description both of electrodynamics and gravity is analyzed.
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry approach developed in [6,7,9], the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. The Dirac-type quantization procedure for the considered alternative electrodynamics models, based on the obtained canonical Hamiltonian formulations, is developed. Comment: 9 pages