A doubler-free lattice theory for QCD based on geometric fermions

TL;DR

This paper introduces a doubler-free, gauge-invariant lattice formulation for QCD using geometric fermions, eliminating the need for correction terms and reducing computational overhead.

Contribution

It proposes a novel geometric representation of the Dirac equation on exterior bundles, leading to doubler-free lattice Dirac operators compatible with Wilson gauge fields.

Findings

Doubler-free lattice Dirac operators for specific bundles.

Gauge-invariant connection with Wilson gauge fields for real representations.

Potential for more efficient lattice QCD simulations without doublers.

Abstract

We present doubler-free gauge-invariant lattice vector gauge action for some real representations of Wilson gauge fields on an octet of fermions. It is based on a geometric representation of the Dirac equation as an evolution equation on the three-dimensional exterior bundle /(R^3) for a single bispinor and of the bundle (/\x/)(R^3) for an octet. We find doubler-free lattice Dirac operators for above bundles. A gauge-invariant connection with Wilson lattice gauge fields is possible for some real representations of the gauge group. The QCD action of SU(3) is of this type. Application in lattice QCD seems useful: We don't have to waste time and memory for doublers as well as for correction terms to suppress them.