CONSERVATIVE EQUATIONS IN FIELD THEORY — CONSERVATION AND SYMMETRY LAWS

The paper introduces a new class of field equations (in Minkowski space), which are called conservative equations. The distinctive features of the introduced equations are their symmetry with respect to transformations with the unitary group U(2) and the presence of additional conservation laws corresponding to the group U(2). A gauge invariant system of equations combining the conservative equation and the Yang–Mills equations is considered. It is proposed to use this system of equations to describe the dynamics of a neutrino with a nonzero mass interacting with the SU(2) Yang–Mills field (field of weak interactions).