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arXiv · 1612.00310

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

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.

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Boris Volkov. 2016-12-01. Levy Differential Operators and Gauge Invariant Equations for Dirac and Higgs Fields. https://doi.org/10.1142/s0219025719500012

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