Supertransvectants and symplectic geometry

Details Supertransvectants and symplectic geometry Supertransvectants and symplectic geometry

2007-05-10

arxiv.org/abs/0705.1411v2

Physics

Mathematical Physics

Scientific paper

We consider the $osp(1|2)$-invariant bilinear operations on weighted densities on the supercircle $S^{1|1}$ called the supertransvectants. These operations are analogues of the famous Gordan transvectants (or Rankin-Cohen brackets). We prove that these operations coincide with the iterated Poisson and ghost Poisson brackets on ${\mathbb R}^{2|1}$ and apply this result to construct star-products involving the supertransvectants.

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