Quantum computational representation of gauge field theory

TL;DR

This paper develops a quantum computing lattice model for a relativistic gauge field theory involving fermions and massive gauge fields, linking curved space and flat space formulations.

Contribution

It introduces a quantum lattice model that encodes fermion spin and gauge interactions via a metric tensor, unifying curved-space and flat-space gauge theories.

Findings

Fermion and gauge fields obey Dirac and Proca equations.

Model reduces to standard quantum field theory in flat space at zero cell size.

Low-energy behavior matches classical equations of motion.

Abstract

Presented is a quantum computing model of a quantum field theory for a system of fermions interacting via a massive gauge field. The model describes a relativistic superconducting fluid and uses a metric tensor field to both encode the fermion's intrinsic spin in the torsion of curved space and encode the coupling of fermions via a massive 4-potential field. The quantum computing model is a lattice model whose cell size is a deformation parameter: the equivalent lattice and curved-space gauge field theory models both reduce to quantum field theory in flat Minkowski space at zero cell size. The low-energy expansions of the lattice model and Euler-Lagrange equations of the curved-space gauge field theory are the same equations of motion. The fermion and gauge fields obey the Dirac and Proca equations, and the gauge field strength is determined by the fermion field.