Non-formal deformation quantizations of solvable Ricci-type symplectic symmetric spaces
(2008) Journal of Physics: Conference Series — Vol. 103, n° 1 (2008)
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- Abstract
- Ricci-type symplectic manifolds have been introduced and extensively studied by M. Cahen et al. [10, 11]. In this note, we describe their deformation quantizations in the split solvable symmetric case. In particular, we introduce the notion of non-formal tempered deformation quantization on such a space. We show that the set of tempered deformation quantizations is in one-to-one correspondence with the space of Schwartz operator multipliers on the real line. Moreover we prove that every invariant formal star product on a split Ricci-type solvable symmetric space is an asymptotic expansion of a tempered non-formal quantization. This note illustrates and partially reviews through an example a problematic studied by the author regarding non-formal quantization in presence of large groups of symmetries.
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Bieliavsky, P. (2008). Non-formal deformation quantizations of solvable Ricci-type symplectic symmetric spaces. Journal of Physics: Conference Series, 103(1). https://doi.org/10.1088/1742-6596/103/1/012001 (Original work published 2008)