Reference : Projectively equivariant quantizations over the superspace R^{p|q}
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/88065
Projectively equivariant quantizations over the superspace R^{p|q}
English
Mathonet, Pierre mailto [University of Luxembourg > FSTC > Mathematics research Unit > >]
Radoux, Fabian mailto [Université de Liège - ULg > Département de mathématique > Géométrie et théorie des algorithmes >]
2011
Letters in Mathematical Physics
Springer Science & Business Media B.V.
98
3
311-331
Yes (verified by ORBi)
International
0377-9017
Dordrecht
The Netherlands
[en] Projectively equivariant quantization ; Supergeometry
[en] We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra pgl(p+1|q) is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields.
Researchers
http://hdl.handle.net/2268/88065
10.1007/s11005-011-0474-0

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