Reference : Natural and Projectively Invariant Quantizations on Supermanifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Natural and Projectively Invariant Quantizations on Supermanifolds
[fr] Quantifications Naturelles et Projectivement Invariantes sur les Supervariétés
Leuther, Thomas mailto [Université de Liège - ULg > > > Doct. sc. (math. - Bologne)]
Radoux, Fabian mailto [Université de Liège - ULg > Département de mathématique > Géométrie et théorie des algorithmes >]
Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA]
SIGMA 7 (2011)
Yes (verified by ORBi)
[en] supergeometry ; differential operators ; quantization maps ; projective invariance
[en] The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m)-equivariant quantization on Rn|m constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two.

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