Abstract:
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.