Stabilized quantum gravity: Stochastic interpretation and numerical simulation

Following the reasoning of Claudson and Halpern, it is shown that "fifth-time" stabilized quantum gravity is equivalent to Langevin evolution (i.e. stochastic quantization) between fixed non-singular, but otherwise arbitrary, initial and final states. The simple restriction to a fixed final state at

t_5 \rightarrow \infty

is sufficient to stabilize the theory. This equivalence fixes the integration measure, and suggests a particular operator-ordering, for the fifth-time action of quantum gravity. Results of a numerical simulation of stabilized, latticized Einstein-Cartan theory on some small lattices are reported. In the range of cosmological constant \l investigated, it is found that: 1) the system is always in the broken phase

<det(e)> \ne 0

; and 2) the negative free energy is large, possibly singular, in the vincinity of \l = 0. The second finding may be relevant to the cosmological constant problem.

quantum gravity
quantization: stochastic
field theory: Euclidean
gauge field theory: Yang-Mills
Chern-Simons term
lattice field theory
numerical calculations: Monte Carlo

References(32)

Figures(0)

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