We study the Lévy infinite-dimensional differential operators (differential operators defined by the analogy with the Lévy 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 connection is a solution to the Yang–Mills equations. This system is an analogue of the equations of motion of chiral fields and contains the Lévy divergence. The systems of infinite-dimensional equations containing Lévy differential operators, that are equivalent to the Yang–Mills–Higgs equations and the Yang–Mills–Dirac equations (the equations of quantum chromodynamics), are obtained. The equivalence of two ways to define Lévy differential operators is shown.

中文翻译：

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狄拉克和希格斯场的 Lévy 微分算子和 Gauge 不变方程

我们研究 Lévy 无限维微分算子（通过与 Lévy Laplacian 类比定义的微分算子）及其与 Yang-Mills 方程的关系。我们将曲线空间上的平行输运视为手性场的无限维模拟，并表明当且仅当关联连接是杨-米尔斯方程的解时，它是微分方程组的解。该系统类似于手征场的运动方程，并包含 Lévy 散度。获得了包含Lévy微分算子的无限维方程组，其等效于Yang-Mills-Higgs方程和Yang-Mills-Dirac方程（量子色动力学方程）。