1996/09/30 by S. Chandrasekharan, U. -J. Wiese · 3 citations
Physics and Astronomy · #hep-lat #cond-mat #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)80041-7
published as Nucl.Phys. B492 (1997) 455-474 · 18 pages, Latex, no figures, final version to appear in Nuclear Physics B, references to earlier work by Horn, Orland and Rohrlich included
arxiv created 1996/12/31 · arxiv updated 2015/06/25
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as quantum spin models are related to ordinary classical spin systems. Here U(1) and SU(2) quantum link models are constructed explicitly. As Hamiltonian theories quantum link models are nonrelativistic gauge theories with potential applications in condensed matter physics. When formulated with a fifth Euclidean dimension, 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 physics, for example to QCD. The configuration space of quantum link models is discrete and hence their numerical treatment should be simpler than that of ordinary lattice gauge theories with a continuous configuration space.