Unitary Representations of the Translational Group Acting as Local Diffeomorphisms of Space-TimeMoffat J*, Oniga T and Wang CHT
Department of Physics, University of Aberdeen, Kingâs College, Aberdeen AB24 3UE, UK
- *Corresponding Author:
- Moffat J
Department of Physics
University of Aberdeen
King’s College, UK
E-mail: [email protected]
Received Date: June 10, 2017; Accepted Date: June 26, 2017; Published Date: June 28, 2017
Citation: Moffat J, Oniga T, Wang CHT (2017) Unitary Representations of the Translational Group Acting as Local Diffeomorphisms of Space-Time. J Phys Math 8: 233. doi: 10.4172/2090-0902.1000233
Copyright: © 2017 Moffat J, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
We continue to develop further a new mathematical approach to the quantisation of general field theories such as general relativity and modified gravity. Treating quantum fields as fibre bundles, we discuss operators acting on each fibre that generate a ‘Fibre Algebra’. The algebras of two types of operators are considered in detail, namely observables as generic physical variables and more specialised quantum operators suitable for describing particles, symmetries and transformations. We then introduce quantum states of these operators and examine their properties. By establishing a link between the commutativity and group cohomology of the translational group as a local gauge group, we show that this leads to unitary representations. of the local gauge group of diffeomorphisms under very general topological conditions; as well the construction of generalised symmetric quantum states invariant under this group action. Discussion of these results in the context of loop quantum gravity and other current theories highlights constraints on the local nature of space-time.