Highly covariant quantum lattice gas model of the Dirac equation

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 τ = 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 (2π{\ell}/λ) and p = (h/2π{\ell}) sin(2π{\ell}/λ), respectively, where λ 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} λ. 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.

5 pages, 2 figures; 66 ABW review on 01 Dec 2010: Ref. No. RVB10.015-198, Case No. 66ABW-2010-1430