Symmetrical structure and conservation relations of four-component neutrino field

Abstract

A four-component spinor field with zero rest-mass ψ is represented as the field defined by its modulus B, an orthogonal frame in two-dimensional internal space, and a Lorentz frame in 4-dimensional internal space. This representation manifests the perfect isotropic property of the field in both internal spaces. In fact, the neutrino equation is invariant under arbitrary rotations in those internal spa es which are conversely expressible by a certain four-component spinor ζ As the result of these new invariance properties the neutrino field is shown to satisfy several conservation relations that are vector or tensor equations with respect to both internal spaces. They contain, besides the conventional ones, a number of new conservation laws.