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.
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}
}
Comments
52p