Deformation quantization of the $n$-tuple point

Details Deformation quantization of the $n$-tuple point Deformation quantization of the $n$-tuple point

1998-10-28

arxiv.org/abs/math/9810158v1

Commun.Math.Phys. 205 (1999) 369-375

Mathematics

Quantum Algebra

LaTeX, 7 pages

Scientific paper

10.1007/s002200050681

Contrary to the classical methods of quantum mechanics, the deformation quantization can be carried out on phase spaces which are not even topological manifolds. In particular, the Moyal star product gives rise to a canonical functor $F$ from the category of affine analytic spaces to the category of associative (in general, non-commutative) $\C$-algebras. Curiously, if $X$ is the $n$-tuple point, $x^{n}=0$, then $F(X)$ is the algebra of $n\times n$ matrices.

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