Mathematics
Scientific paper
Mar 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cqgra...6..275r&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 6, March 1, 1989, p. 275-294. Research supported by NASA.
Mathematics
35
Gravitation Theory, Lattices (Mathematics), Quantum Mechanics, Relativity, Spinor Groups, Continuity (Mathematics), Gauge Theory, Gravitational Fields, Hilbert Space
Scientific paper
A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.
Renteln Paul
Smolin Lee
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