Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-11-17
J.Math.Phys.51:092501,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages
Scientific paper
10.1063/1.3486359
Canonical quantisation of constrained systems with first class constraints via Dirac's operator constraint method proceeds by the thory of Rigged Hilbert spaces, sometimes also called Refined Algebraic Quantisation (RAQ). This method can work when the constraints form a Lie algebra. When the constraints only close with nontrivial structure functions, the Rigging map can no longer be defined. To overcome this obstacle, the Master Constraint Method has been proposed which replaces the individual constraints by a weighted sum of absolute squares of the constraints. Now the direct integral decomposition methods (DID), which are closely related to Rigged Hilbert spaces, become available and have been successfully tested in various situations. It is relatively straightforward to relate the Rigging Inner Product to the path integral that one obtains via reduced phase space methods. However, for the Master Constraint this is not at all obvious. In this paper we find sufficient conditions under which such a relation can be established. Key to our analysis is the possibility to pass to equivalent, Abelian constraints, at least locally in phase space. Then the Master Constraint DID for those Abelian constraints can be directly related to the Rigging Map and therefore has a path integral formulation.
Han Muxin
Thiemann Thomas
No associations
LandOfFree
On the Relation between Rigging Inner Product and Master Constraint Direct Integral Decomposition does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the Relation between Rigging Inner Product and Master Constraint Direct Integral Decomposition, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Relation between Rigging Inner Product and Master Constraint Direct Integral Decomposition will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-240121