Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-09-12
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, 8 figures
Scientific paper
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional piecewise linear spaces, with the solutions to the lattice equations providing a suitable approximation to the continuum wave functional. The equations incorporate a set of constraints on the quantum wavefunctional, arising from the triangle inequalities and their higher dimensional analogs. The character of the solutions is discussed in the strong coupling (large $G$) limit, where it is shown that the wavefunctional only depends on geometric quantities, such as areas and volumes. An explicit form, determined from the discrete wave equation supplemented by suitable regularity conditions, shows peaks corresponding to integer multiples of a fundamental unit of volume. An application of the variational method using correlated product wavefunctions suggests a relationship between quantum gravity in $n+1$ dimensions, and averages computed in the Euclidean path integral formulation in $n$ dimensions. The proposed discrete equations could provide a useful, and complementary, computational alternative to the Euclidean lattice path integral approach to quantum gravity.
Hamber Herbert W.
Williams Ruth M.
No associations
LandOfFree
Discrete Wheeler-DeWitt Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Discrete Wheeler-DeWitt Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete Wheeler-DeWitt Equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-60491