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Matrix Cartan Superdomains, Super Toeplitz Operators, and Quantization


Journal Title:

Journal of Functional Analysis


Volume 127


, Pages 456-510

Type of Work:

Article | Preprint: Prior to Peer Review


We present a general theory of non-perturbative quantization of a class of hermitian symmetric supermanifolds. The quantization scheme is based on the notion of a super Toeplitz operator on a suitable 2-graded Hilbert spaces of super-holomorphic functions. The quantized supermanifold arises as the *-algebra generated by all such operators. We prove that our quantization framework reproduces the invariant super Poisson structure on the classical supermanifold as Planck′s constant tends to zero.

Copyright information:

© 1995 Academic Press

This is an Open Access work distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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