Lattice Quantization of Free Fermions without Doublers

TL;DR

This paper introduces a lattice quantization method for free fermions that removes fermion doublers across dimensions by combining second-order descriptions with non-Hermitian Hamiltonian tools.

Contribution

It presents a novel approach to eliminate fermion doublers on the lattice using pseudo-Hermitian symmetry and second-order fermion equations.

Findings

Successfully eliminates fermion doublers in numerical simulations.

Identifies a new pseudo-Hermitian symmetry in second-order fermion equations.

Connects the symmetry to a $U(1)$ charge symmetry for gauge theories.

Abstract

We present a method to quantize free fermions which eliminates the doublers when implemented on the lattice in any number of dimensions and in the $m=0$ limit. The elimination of doublers is achieved by combining a second-order description of fermions, with the tools associated with non-Hermitian Hamiltonians. We identify a new Pseudo-Hermitian symmetry of the second-order fermion equation, and we identify the associated $U(1)$ symmetry which will become charge when shifted to a local gauge theory. We validated the methods numerically.