Chirally Invariant Avatar in a Model of Neutrinos with Light Cone Reflection Symmetry

TL;DR

This paper constructs a two-dimensional model preserving light cone reflection and chiral symmetry from a four-dimensional neutrino model, maintaining gauge invariance and exploring scalar field determination.

Contribution

It introduces a two-dimensional avatar of a neutrino model with Light Cone Reflection symmetry, preserving key symmetries and gauge invariance from the original four-dimensional theory.

Findings

Successfully constructed a 2D model obeying the same equations as the 4D model.

Maintained light-cone reflection and chiral symmetries in the 2D avatar.

Discussed how to determine the scalar field in the LCR-covariant derivative.

Abstract

In previous work we developed a model of neutrinos based on a new symmetry, Light Cone Reflection (LCR), that interchanges spacelike and timelike intervals. In this paper we start with the four-dimensional model, and construct a two-dimensional avatar that obeys the same equations of motion, and preserves both the light-cone reflection symmetry and the chiral symmetry of the original theory. The avatar also contains the interaction that rendered the four-dimensional model gauge invariant. In an addendum, we make some remarks about how to determine the scalar field that enters into the definition of the LCR-covariant derivative.