Quantum Gravity

It is one of the main open problems of physics to find a quantum theory of gravitation.

My contribution focused on quantum gravity defined on simplicial lattices using the

Regge calculus [1]. Some of my papers are listed below,

hep-lat/0309002

hep-lat/9602009

hep-lat/9505002

hep-lat/9412073

hep-lat/9402002

a complete list is available at hep-spires.

The main finding is the existence of a phase with well defined expectation values [2].

However, an interesting continuum limit would require a 2nd order phase transition [3],

but so far such a transition has not been found [4].

Recently, Seth Lloyd has proposed to view our universe as a quantum computer and this

approach leads to a variant of Regge quantum gravity defined on simplicial lattices.

Several other proposals have been suggested to solve the mysteries of quantum gravity,

the most promising being M-theory, which is a unified theory of superstrings.

One can only hope that new empirical evidence will help us find the correct solution.

[1] The review talk of Des Johnston and the living review of Renate Loll provide for

overviews and an introduction to lattice quantum gravity.

[2] I should mention the work of Martin Pilati [1,2,3]; He found an exact solution for the

strong-coupling limit G -> infinity. The solution uses the fact that in quantum gravity the

strong-coupling limit is equivalent to the limit c = 0, so that all light cones collapse and

different points in space decouple. Different lattice gravity models exhibit a "well-defined"

phase for strong-coupling.

[3] Jacques Distler discussed the continuum limit of lattice gravity models (in the context

of CDT) here and the related issue of the UV fixed point here.

[4] The paper hep-lat/9407020 examines the Regge approach on non-regular triangulated

lattices and the results clearly indicate problems to find a continuum limit.

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