Nonperturbative quantization approach for qed on the hopf bundle†
Dzhunushaliev V. Folomeev V.
2021MDPI AG
Universe
2021#7Issue 3
We consider the Dirac equation and Maxwell’s electrodynamics in R × S3 spacetime, where a three-dimensional sphere is the Hopf bundle S3 → S2 . In both cases, discrete spectra of classical solutions are obtained. Based on the solutions obtained, the quantization of free, noninteracting Dirac and Maxwell fields is carried out. The method of nonperturbative quantization of interacting Dirac and Maxwell fields is suggested. The corresponding operator equations and the infinite set of the Schwinger–Dyson equations for Green’s functions is written down. We write a simplified set of equations describing some physical situations to illustrate the suggested scheme of nonper-turbative quantization. Additionally, we discuss the properties of quantum states and operators of interacting fields.
Classical solutions , Dirac equation , Discrete spectrum , Hopf bundle , Maxwell’s electrodynamics , Nonperturbative quantization
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Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Department of Theoretical and Nuclear Physics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Academician J. Jeenbaev Institute of Physics of the NAS of the Kyrgyz Republic, 265 a, Chui Street, Bishkek, 720071, Kyrgyzstan
International Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), Tomsk, 634050, Russian Federation
Institute of Experimental and Theoretical Physics
Department of Theoretical and Nuclear Physics
Academician J. Jeenbaev Institute of Physics of the NAS of the Kyrgyz Republic
International Laboratory for Theoretical Cosmology
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