A Ginsparg-Wilson approach to lattice CP symmetry, Weyl and Majoranna fermions, and the Higgs mechanism

TL;DR

This paper integrates two approaches to address lattice CP symmetry issues, formulates Weyl and Majorana fermions on the lattice, and explores implications for fermion propagators with the Higgs field, advancing lattice gauge theory methods.

Contribution

It combines existing solutions into a unified framework based on the renormalisation group, and extends lattice formulations to Weyl and Majorana fermions with applications to the Higgs mechanism.

Findings

Unified framework for lattice CP symmetry solutions.

Formulation of Weyl and Majorana fermions on the lattice.

Analysis of fermion propagator with Higgs field.

Abstract

Recently, two solutions have been proposed to the long standing problem of $\mathcal{CP}$-symmetry on the lattice, which is particularly evident when considering the construction of chiral gauge theories. The first, based on a lattice modification of $\mathcal{CP}$ was presented by Igarashi and Pawlowski; the second by myself using the renormalisation group and Ginsparg-Wilson relation. In this work, I combine the two approaches and show that they are each part of a more general framework related to an underlying renormalisation group. I continue by formulating Weyl and Majorana fermions on the lattice, and discussing applications to the fermion propagator in the presence of the Higgs field.