# Finite-element quantum field theory

## TL;DR

This paper presents a novel finite-element approach to quantum field theory that discretizes operator equations of motion, preserving canonical relations and avoiding fermion doubling, offering a promising alternative to lattice gauge theory.

## Contribution

It introduces a finite-element framework for non-Abelian gauge theories that maintains unitarity and canonical commutation relations, addressing limitations of traditional lattice methods.

## Key findings

- Formulation of non-Abelian gauge theory within finite-element framework
- Preservation of canonical commutation relations at each lattice site
- Avoidance of fermion doubling problem

## Abstract

An alternative approach to lattice gauge theory has been under development for the past decade. It is based on discretizing the operator Heisenberg equations of motion in such a way as to preserve the canonical commutation relations at each lattice site. It is now known how to formulate a non-Abelian gauge theory within this framework. The formulation appears to be free of fermion doubling. Since the theory is unitary, a time-development operator (Hamiltonian) can be constructed.