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

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.