THE QCD ABACUS: A New Formulation for Lattice Gauge Theories

Abstract

A quantum Hamiltonian is constructed for SU(3) lattice QCD entirely from color triplet Fermions --- the standard quarks and a new Fermionic ``constituent'' of the gluon we call ``rishons''. The quarks are represented by Dirac spinors on each site and the gauge fields by rishon-antirishon bilinears on each link which together with the local gauge transforms are the generators of an SU(6) algebra. The effective Lagrangian for the path integral lives in $R^4 \times S^1$ Euclidean space with a compact ``fifth time'' of circumference ($β$) and non-Abelian charge ($e^2$) both of which carry dimensions of length. For large $β$, it is conjectured that continuum QCD is reached and that the dimensionless ratio $g^2 = e^2/β$ becomes the QCD gauge coupling. The quarks are introduced as Kaplan chiral Fermions at either end of the finite slab in fifth time. This talk will emphasize the gauge and algebraic structure of the rishon or link Fermions and the special properties that may lead to fast discrete dynamics for numerical simulations and new theoretical insight.