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Mathematical Physics

arXiv:1612.00310 (math-ph)
[Submitted on 1 Dec 2016 (v1), last revised 29 Jul 2018 (this version, v2)]

Title:Levy Differential Operators and Gauge Invariant Equations for Dirac and Higgs Fields

Authors:Boris Volkov
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Abstract:We study the Levy infinite-dimensional differential operators (differential operators defined by the analogy with the Levy Laplacian) and their relationship to the Yang-Mills equations. We consider the parallel transport on the space of curves as an infinite-dimensional analogue of chiral fields and show that it is a solution to the system of differential equations if and only if the associated curvature is a solution to the Yang-Mills equations. This system is an analogue of the equation of motion of chiral fields and contains the Levy divergence. The systems of infinite-dimensional equations containing Levy differential operators, that are equivalent to the Yang-Mills-Higgs equations and the Yang-Mills-Dirac equations (the equations of quantum chromodinamics), are obtained. The equivalence of two ways to define the Levy differential operators is shown.
Comments: 23 pages. The conclusion and some referrences are added. Some minor changes
Subjects: Mathematical Physics (math-ph)
MSC classes: 70S15
Cite as: arXiv:1612.00310 [math-ph]
  (or arXiv:1612.00310v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1612.00310
Journal reference: Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 22, No. 1 (2019) 1950001 (20 pages)
Related DOI: https://doi.org/10.1142/S0219025719500012

Submission history

From: Boris Volkov [view email]
[v1] Thu, 1 Dec 2016 15:27:16 UTC (17 KB)
[v2] Sun, 29 Jul 2018 10:20:50 UTC (15 KB)
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