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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