Propagating spinors on a tetrahedral spacetime lattice

TL;DR

This paper develops a discrete path integral formulation for massless fermions on a tetrahedral spacetime lattice with null faces, providing a new way to simulate fermionic fields in discretized spacetime.

Contribution

It introduces a novel discrete path integral approach for massless fermions on a tetrahedral lattice with null faces, expanding lattice field theory methods.

Findings

Derived the path integral amplitude formula for fermion paths with N steps and B bends

Demonstrated the applicability of the method to null-faced tetrahedral lattices

Provides a foundation for future numerical simulations of fermions in discretized spacetime

Abstract

We derive a discrete path integral for massless fermions on a hypercubic spacetime lattice with null faces. The amplitude for a path with N steps and B bends is +/- (1/2)^N (i/sqrt{3})^B.