The search for solutions was continued by Ezawa [99] (see also [100] for an extensive review), who used a symmetrized form of the
Hamiltonian. His solutions depend on multiple plaquette loops
, where a single lattice plaquette
is traversed by the loop
k
times. The solutions are less trivial than those formed from
Polyakov loops, since they involve kinks, but they are still
annihilated by the volume operator.
A somewhat different strategy was followed by Fort et al [102], who constructed a Hamiltonian lattice regularization for the calculation of certain knot invariants. They defined lattice constraint operators in terms of their geometric action on lattice Wilson loop states, and reproduced some of the formal continuum solutions to the polynomial Hamiltonian constraint of complex Ashtekar gravity on simple loop geometries.
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Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll http://www.livingreviews.org/lrr-1998-13 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |