The QCD abacus: A cellular automata formulation for continuous gauge symmetries

Abstract

This talk will explain a new way to formulate statistical (or quantum field) theories entirely in terms discrete quantum spins. Remarkably even theorieswith continuous symmetries such as 3-d rotations can be exactly represented in such a discrete (or binary) “computational” framework. A new application of this idea to Quantum Chromodynamics (QCD), the fundamental gauge theory for nuclear forces, is presented. Here a classical theory with commuting (Bosonic) fields is replaced by anti-commuting (Fermionic) variables acting in an extra 5-th dimension. The effective Lagrangian for the path integral lives in R4 X S1 Euclidean manifold with a compact “fifth time” of circumference L and non-Abelian charge (e2) both of which carry dimensions of length. For large (but finite) L, it is argued that continuum limit is reached and that the dimensionless ratio g2 = e2/L becomes the QCD gauge coupling. This talk wilt emphasize general concepts and intuitive methods that hopefully can be applied to a wide class of quantum cellular automata and the general algebraic structure that can lead to fast cluster algorithms for Monte Carlo simulations.