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#### Wheeler-DeWitt Equation in 3 + 1 Dimensions

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##### Fulltext (public)

1212.3492

(Preprint), 14MB

PhysRevD.88.084012.pdf

(Any fulltext), 2MB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Hamber, H. W., Toriumi, R., & Williams, R. M. (2013). Wheeler-DeWitt Equation in
3 + 1 Dimensions.* Physical Review D,* *88*(8): 084012.
doi:10.1103/PhysRevD.88.084012.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000E-77FE-6

##### Abstract

Physical properties of the quantum gravitational vacuum state are explored by
solving a lattice version of the Wheeler-DeWitt equation. The constraint of
diffeomorphism invariance is strong enough to uniquely determine the structure
of the vacuum wave functional in the limit of infinitely fine triangulations of
the three-sphere. In the large fluctuation regime the nature of the wave
function solution is such that a physically acceptable ground state emerges,
with a finite non-perturbative correlation length naturally cutting off any
infrared divergences. The location of the critical point in Newton's constant
$G_c$, separating the weak from the strong coupling phase, is obtained, and it
is inferred from the structure of the wave functional that fluctuations in the
curvatures become unbounded at this point. Investigations of the vacuum wave
functional further indicate that for weak enough coupling, $G< G_c$, a
pathological ground state with no continuum limit appears, where configurations
with small curvature have vanishingly small probability. One is then lead to
the conclusion that the weak coupling, perturbative ground state of quantum
gravity is non-perturbatively unstable, and that gravitational screening cannot
be physically realized in the lattice theory. The results we find are in
general agreement with the Euclidean lattice gravity results, and lend further
support to the claim that the Lorentzian and Euclidean lattice formulations for
gravity describe the same underlying non-perturbative physics.