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Matrix Cartan superdomains, super Toeplitz operators, and quantization

D. Borthwick·S. Klimek·A. Lesniewski·M. Rinaldi
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Abstract

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 Z_2 -graded Hilbert space of superholomorphic functions. The quantized supermanifold arises as the C^* -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.

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D. Borthwick, S. Klimek, A. Lesniewski, M. Rinaldi. 1994-06-09. Matrix Cartan superdomains, super Toeplitz operators, and quantization. https://arxiv.org/abs/hep-th/9406050

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