Nonperturbative solutions for lattice quantum gravity
Jan, 199525 pages
Published in:
- Nucl.Phys.B 444 (1995) 619-640
e-Print:
- gr-qc/9502006 [gr-qc]
Report number:
- DFF-220-01-95
View in:
Citations per year
Abstract: (Elsevier)
We propose a new, discretized model for the study of (3 + 1)-dimensional canonical quantum gravity, based on the classical SL(2, C )-connection formulation. The discretization takes place on a topological N 3 lattice with periodic boundary conditions. All operators and wave functions are constructed from one-dimensional link variables, which are regarded as the fundamental building blocks of the theory. The kinematical Hilbert space is spanned by polynomials of certain Wilson loops on the lattice and is manifestly gauge- and diffeomorphism-invariant. The discretized quantum Hamiltonian H ̆ maps this space into itself. We find a large sector of solutions to the discretized Wheeler-DeWitt equation H ̆ ψ = 0 , which are labelled by single and multiple Polyakov loops. These states have a finite norm with respect to a natural scalar product on the space of holomorphic SL(2, C) -Wilson loops. We also investigate the existence of further solutions for the case of the 1 3 lattice. Our results provide for the first time a rigorous, regularized framework for studying non-perturbative canonical quantum gravity.Note:
- 26 pages, 2 figures (postscript, compressed and uuencoded), TeX, Jan 95 Report-no: DFF 220/01/95
- quantum gravity
- gauge field theory: SU(2)
- lattice field theory
- linear space: Hilbert space
- Wilson loop
- Wheeler-DeWitt equation: solution
- nonperturbative
- Hamiltonian formalism
- symmetry: SL(2,C)
- Polyakov loop
References(24)
Figures(0)