Matrix Cartan superdomains, super Toeplitz operators, and quantization

Details Matrix Cartan superdomains, super Toeplitz operators, and quantization Matrix Cartan superdomains, super Toeplitz operators, and quantization

1994-06-09

arxiv.org/abs/hep-th/9406050v1

Physics

High Energy Physics

High Energy Physics - Theory

52p

Scientific paper

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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