QUANTUM LINK MODELS - A DISCRETE APPROACH TO GAUGE-THEORIES

We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilber t space. These quantum link models are related to ordinary lattice gau ge theories in the same way as quantum spin models are related to ordi nary classical spin systems. Here U(1) and SU(2) quantum link models a re constructed explicitly. As Hamiltonian theories quantum link models are non-relativistic gauge theories with potential applications in co ndensed matter physics, When formulated with a fifth Euclidean dimensi on, universality arguments suggest that dimensional reduction to four dimensions occurs, Hence, quantum link models are also reformulations of ordinary quantum field theories and are applicable to particle phys ics, for example to QCD. The configuration space of quantum link model s is discrete and hence their numerical treatment should be simpler th an that of ordinary lattice gauge theories with a continuous configura tion space. (C) 1997 Published by Elsevier Science B.V.