A matrix-valued Berezin-Toeplitz quantization

Details A matrix-valued Berezin-Toeplitz quantization A matrix-valued Berezin-Toeplitz quantization

2006-11-29

arxiv.org/abs/math-ph/0611082v1

Physics

Mathematical Physics

15 pages, no pictures

Scientific paper

We generalize some earlier results on a Berezin-Toeplitz type of quantization on Hilbert spaces built over certain matrix domains. In the present, wider setting, the theory could be applied to systems possessing several kinematic and internal degrees of freedom. Our analysis leads to an identification of those observables, in this general context, which admit a semi-classical limit and those for which no such limit exists. It turns out that the latter class of observables involve the internal degrees of freedom in an intrinsic way. Mathematically, the theory, being a generalization of the standard Berezin-Toeplitz quantization, points the way to applying such a quantization technique to possibly non-commutative spaces, to the extent that points in phase space are now replaced by $N\times N$ matrices.

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