Levy Differential Operators and Gauge Invariant Equations for Dirac and Higgs Fields
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.
Keywords
Cite
@article{arxiv.1612.00310,
title = {Levy Differential Operators and Gauge Invariant Equations for Dirac and Higgs Fields},
author = {Boris Volkov},
journal= {arXiv preprint arXiv:1612.00310},
year = {2019}
}
Comments
23 pages. The conclusion and some referrences are added. Some minor changes