English

Matrix Cartan superdomains, super Toeplitz operators, and quantization

High Energy Physics - Theory 2009-09-25 v1

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.

Keywords

Cite

@article{arxiv.hep-th/9406050,
  title  = {Matrix Cartan superdomains, super Toeplitz operators, and quantization},
  author = {D. Borthwick and S. Klimek and A. Lesniewski and M. Rinaldi},
  journal= {arXiv preprint arXiv:hep-th/9406050},
  year   = {2009}
}

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