Quantization by cochain twists and nonassociative differentials
- Department of Mathematics, University of Wales, Swansea SA2 8PP (United Kingdom)
- School of Mathematical Sciences, Queen Mary University of London, 327 Mile End Rd., London E1 4NS (United Kingdom)
We show that several standard associative quantizations in mathematical physics can be expressed as cochain module-algebra twists in the spirit of Moyal products at least to O(({Dirac_h}/2{pi}){sup 3}), but to achieve this we twist not by a 2-cocycle but by a 2-cochain. This implies a hidden nonassociativity not visible in the algebra itself but present in its deeper noncommutative differential geometry, a phenomenon first seen in our previous work on semiclassicalization of differential structures. The quantizations are induced by a classical group covariance and include enveloping algebras U(g) as quantizations of g*, a Fedosov-type quantization of the sphere S{sup 2} under a Lorentz group covariance, the Mackey quantization of homogeneous spaces, and the standard quantum groups C{sub q}[G]. We also consider the differential quantization of R{sup n} for a given symplectic connection as part of our semiclassical analysis and we outline a proposal for the Dirac operator.
- OSTI ID:
- 21335972
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 5; Other Information: DOI: 10.1063/1.3371677; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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