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tom.stoer
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In the thread https://www.physicsforums.com/showthread.php?t=485800&page=17 posz #257 fzero mentions that
all known approaches to use gauge theory to describe canonical gravity fail nonperturbatively (Witten in http://arxiv.org/abs/0706.3359 "Three-Dimensional Gravity Revisited"):
- gauge theories always include solutions where the vierbein is not invertible (not visible perturbatively)
- gauge theory only describes diffeomorphisms which are connected to the identity
fzero concludes that any attempt to formulate quantum gravity as a gauge theory in which there is a canonical map between degrees of freedom is incomplete
I would like to ask if and how this affects LQG (both in the old-fashioned approach where one uses Ashtekar and loop variables for quantization and in the new approach where one omits quantization in the sense of a construction and postulates spin networks as the kinematical basis for LQG)
In addition I would like to ask how this is different for "ordinary" gauge theory (e.g. in the canonical or BRST approach) as we know that these formulations have similar problems, e.g. singular gauge field confugurations due to Gribov copies etc., visible only non-perturbatively.
Then I would like to ask if this is a problem at all as we typically see such singular configurations already in ordinary quantum mechanics, but usually the system cures this via "repulsive potentials" and "boundary conditions" (orbital angular momentum in hydrogen atom, QCD in canonical formulation with "repulsive" terms due to Jacobian = Fadeev-Popov determinant, ...).
all known approaches to use gauge theory to describe canonical gravity fail nonperturbatively (Witten in http://arxiv.org/abs/0706.3359 "Three-Dimensional Gravity Revisited"):
- gauge theories always include solutions where the vierbein is not invertible (not visible perturbatively)
- gauge theory only describes diffeomorphisms which are connected to the identity
fzero concludes that any attempt to formulate quantum gravity as a gauge theory in which there is a canonical map between degrees of freedom is incomplete
I would like to ask if and how this affects LQG (both in the old-fashioned approach where one uses Ashtekar and loop variables for quantization and in the new approach where one omits quantization in the sense of a construction and postulates spin networks as the kinematical basis for LQG)
In addition I would like to ask how this is different for "ordinary" gauge theory (e.g. in the canonical or BRST approach) as we know that these formulations have similar problems, e.g. singular gauge field confugurations due to Gribov copies etc., visible only non-perturbatively.
Then I would like to ask if this is a problem at all as we typically see such singular configurations already in ordinary quantum mechanics, but usually the system cures this via "repulsive potentials" and "boundary conditions" (orbital angular momentum in hydrogen atom, QCD in canonical formulation with "repulsive" terms due to Jacobian = Fadeev-Popov determinant, ...).