Proca tubes with the flux of the longitudinal chromoelectric field and the energy flux/momentum density
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Regular Article - Theoretical Physics
Proca tubes with the flux of the longitudinal chromoelectric field and the energy flux/momentum density Vladimir Dzhunushaliev1,2,3,a , Vladimir Folomeev2,3,4,b 1
Department of Theoretical and Nuclear Physics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan 3 Academician J. Jeenbaev Institute of Physics of the NAS of the Kyrgyz Republic, 265 a, Chui Street, Bishkek 720071, Kyrgyzstan 4 International Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), Tomsk 634050, Russia
2
Received: 24 May 2020 / Accepted: 31 October 2020 © The Author(s) 2020
Abstract We consider non-Abelian SU(3) Proca theory with a Higgs scalar field included. Cylindrically symmetric solutions describing classical tubes either with the flux of a longitudinal electric field or with the energy flux (and hence with nonzero momentum density) are obtained. It is shown that, in quantum Proca theory, there can exist tubes both with the flux of the longitudinal electric field and with the energy flux/momentum density simultaneously. An imaginary particle – Proca proton – in which ‘quarks’ are connected by tubes with nonzero momentum density is considered. It is shown that this results in the appearance of the angular momentum related to the presence of the non-Abelian electric and magnetic fields in the tube, and this angular momentum is a part of the Proca proton spin.
1 Introduction In recent years there is a growing interest in modelling systems containing various massive vector fields. Such fields are described within gauge Proca theories (both Abelian and non-Abelian ones) where the gauge invariance is violated explicitly by introducing a mass term. Being the generalization of Maxwell’s theory, Proca theory permits one to take into account various effects related to the possible presence of the mass of vector particles. At the present time, Proca fields are used in different aspects: in constructing models of black holes [1], hypothetical Proca stars [2–5], in studying the generalized Proca theories [6–8] and solitons [9], in describing the massive spin-1 Z 0 and W ± bosons in the standard model [10], in considering various effects related to a e-mail:
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the possible presence of the rest mass of a photon [11], and within dark matter physics [12]. When considering configurations containing Proca fields, the main efforts have been focused on studying spherically symmetric solutions. However, a consideration of cylindrically symmetric systems seems to be of interest as well. In particular, cylindrically symmetric localized regular solutions (the so-called ‘Proca Q tubes’) have been found in Ref. [13]. The next natural step in this direction is to generalize systems containing Proca fields by including extra fields in them.
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