2010/10/31 by Thomas Leuther, Fabian Radoux
Mathematics · Physics and Astronomy · #math-ph #math.DG #math.MP #msc:53B05 #msc:53B10 #msc:53D50 #msc:58A50
paper · pdf · doi:10.3842/sigma.2011.034
published as SIGMA 7:034,2011
arxiv created 2011/03/31 · arxiv updated 2011/04/05
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 \mathfrakpgl(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.