Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1996-09-26
Nucl.Phys. B492 (1997) 455-474
Physics
High Energy Physics
High Energy Physics - Lattice
18 pages, Latex, no figures, final version to appear in Nuclear Physics B, references to earlier work by Horn, Orland and Rohr
Scientific paper
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.
Chandrasekharan Shailesh
Wiese Uwe-Jens
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