Highly covariant quantum lattice gas model of the Dirac equation

TL;DR

This paper introduces a covariant quantum lattice gas model for the Dirac equation that accurately captures relativistic properties at small scales and reveals novel relations for mass and momentum, with implications for vacuum energy.

Contribution

It presents a new covariant quantum lattice gas model for the Dirac equation with scale-dependent mass and momentum relations, improving physical accuracy at small scales.

Findings

Model is covariant under Lorentz transformations at all scales.

Derived scale-dependent relations for mass and momentum.

Vacuum energy for massless fields can vanish or be small positive.

Abstract

We revisit the quantum lattice gas model of a spinor quantum field theory-the smallest scale particle dynamics is partitioned into unitary collide and stream operations. The construction is covariant (on all scales down to a small length {\ell} and small time {\tau} = c {\ell}) with respect to Lorentz transformations. The mass m and momentum p of the modeled Dirac particle depend on {\ell} according to newfound relations m = mo cos (2{\pi}{\ell}/{\lambda}) and p = (h/2{\pi}{\ell}) sin(2{\pi}{\ell}/{\lambda}), respectively, where {\lambda} is the Compton wavelength of the modeled particle. These relations represent departures from a relativistically invariant mass and the de Broglie relation-when taken as quantifying numerical errors the model is physically accurate when {\ell} {\ll} {\lambda}. Calculating the vacuum energy in the special case of a massless spinor field, we find that it vanishes (or can have a small positive value) for a sufficiently large wave number cutoff. This is a marked departure from the usual behavior of such a massless field.