A Covariant Poisson Deformation Quantization with Separation of Variables up to the Third Order |
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Authors: | Karabegov Alexander |
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Affiliation: | (1) Department of Mathematics and Computer Science, Abilene Christian University, Acu Box 28012, 252 Foster Science Building, Abilene, TX, 79649–8012, U.S.A. |
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Abstract: | We give a simple formula for the operator C3 of the standard deformation quantization with separation of variables on a Kähler manifold M. Unlike C1 and C2, this operator cannot be expressed in terms of the Kähler–Poisson tensor on M. We modify C3 to obtain a covariant deformation quantization with separation of variables up to the third order which is expressed in terms of the Poisson tensor on M and can thus be defined on an arbitrary complex manifold endowed with a Poisson bivector field of type (1,1). |
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Keywords: | deformation quantization Kä hler connection poisson tensor |
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