The Deformation Quantization of $\Real^n$ via the specifiaction of the commutators

Details The Deformation Quantization of $\Real^n$ via the specifiaction of the commutators The Deformation Quantization of $\Real^n$ via the specifiaction of the commutators

2004-11-25

arxiv.org/abs/math/0411581v1

Mathematics

Quantum Algebra

14 pages, no figures. Permanent address: j@gratus.net www.gratus.net

Scientific paper

In a deformation quantization of $\Real^n$, the Jacobi identity is automatically satisfied. This article poses the contrary question: Given a set of commutators which satisfies the Jacobi identity, is the resulting associative algebra a deformation quantization of $\Real^n$? It is shown that the result is true. However care must taken when stating precisely how and in which algebra the Jacobi identity is satisfied.

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