Аннотация:
The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [<i>Progr. Theoret. Phys. Suppl.</i> (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.
\RBibitem{LeuRad11}
\by Thomas Leuther, Fabian Radoux
\paper Natural and Projectively Invariant Quantizations on Supermanifolds
\jour SIGMA
\yr 2011
\vol 7
\papernumber 034
\totalpages 12
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\crossref{https://doi.org/10.3842/SIGMA.2011.034}
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Эта публикация цитируется в следующих 7 статьяx:
Calvin Mera Sánchez, Vincent G. J. Rodgers, Patrick Vecera, “Graded extension of Thomas-Whitehead gravity”, Phys. Rev. D, 106:8 (2022)
Bichr T., Boujelben J., Saoudi Z., Tounsi K., “Modules of N-Ary Differential Operators Over the Orthosymplectic Superalgebra Osp(1 Vertical Bar 2)”, Proc. Indian Acad. Sci.-Math. Sci., 131:1 (2021), 11
Bruce A.J., Grabowski J., “Odd Connections on Supermanifolds: Existence and Relation With Affine Connections”, J. Phys. A-Math. Theor., 53:45 (2020), 455203
Bichr T., Boujelben J., Tounsi Kh., “Modules of Bilinear Differential Operators Over the Orthosymplectic Superalgebra Osp (1 Vertical Bar 2)”, Tohoku Math. J., 70:2 (2018), 319–338
Leuther T., Radoux F., Tuynman G.M., “Geodesics on a Supermanifold and Projective Equivalence of Superconnections”, J. Geom. Phys., 67 (2013), 81–96
Najla Mellouli, Aboubacar Nibirantiza, Fabian Radoux, “$\mathfrak{spo}(2|2)$-Equivariant Quantizations on the Supercircle $S^{1|2}$”, SIGMA, 9 (2013), 055, 17 pp.
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