An explicit formula for the Berezin star product

Abstract

We prove an explicit formula of the Berezin star product on Kaehler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Englis' work on the asymptotic expansion of the Laplace integral.

19 pages, to appear in Lett. Math. Phys

References in corpus (1)

• Toeplitz operators on symplectic manifolds

Cited by in corpus (6)

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• Scaling asymptotics of Szego kernels under commuting Hamiltonian actions
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• Weyl invariant polynomial and deformation quantization on Kahler manifolds
• On Gammelgaard's formula for a star product with separation of variables
• Deformation quantization with separation of variables of an endomorphism bundle