Matrix Cartan Superdomains, Super Toeplitz-Operators, and Quantization

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 Z2-graded Hilbert spaces of super-holomorphic functions. The quantized supermanifold arises as the...

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Bibliographic Details
Published in:	Journal of functional analysis Vol. 127; no. 2; pp. 456 - 510
Main Authors:	Borthwick, D., Klimek, S., Lesniewski, A., Rinaldi, M.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.02.1995
ISSN:	0022-1236, 1096-0783
Online Access:	Get full text
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Summary:	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 Z2-graded Hilbert spaces of super-holomorphic 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.
ISSN:	0022-1236 1096-0783
DOI:	10.1006/jfan.1995.1020