Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-05-18
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
22 pages, 2 figures
Scientific paper
In this paper, we are going to discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional General Relativity and Supergravity developed in our companion papers. Since the canonical quadratic simplicity constraint operators have been shown to be anomalous in any dimension D > 2, non-standard methods have to be employed to avoid inconsistencies in the quantum theory. We show that one can choose a subset of quadratic simplicity constraint operators which are non-anomalous among themselves and allow for a natural unitary 1-1 map to the SU(2)-based Ashtekar-Lewandowski Hilbert space in D = 3. The linear constraint operators on the other hand are non-anomalous by themselves, however their solution space will be shown to differ in D = 3 from the expected Ashtekar-Lewandowski Hilbert space. We comment on possible strategies to make a connection to the quadratic theory. We emphasise that many ideas developed in this paper are certainly incomplete and should be considered as suggestions for possible starting points for more satisfactory treatments in the future.
Bodendorfer Norbert
Thiemann Thomas
Thurn Andreas
No associations
LandOfFree
On the Implementation of the Canonical Quantum Simplicity Constraint 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 Implementation of the Canonical Quantum Simplicity Constraint, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Implementation of the Canonical Quantum Simplicity Constraint will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-54579