151. Orderings and Non-formal Deformation Quantization
- Author
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Akira Yoshioka, Naoya Miyazaki, Hideki Omori, and Yoshiaki Maeda
- Subjects
Algebra ,Geometric quantization ,Canonical quantization ,Quantization (signal processing) ,Independence (mathematical logic) ,Statistical and Nonlinear Physics ,Convergence problem ,Star (graph theory) ,Deformation (meteorology) ,Second quantization ,Mathematical Physics ,Mathematics - Abstract
We propose suitable ideas for non-formal deformation quantization of Frechet Poisson algebras. To deal with the convergence problem of deformation quantization, we employ Frechet algebras originally given by Gel’fand–Shilov. Ideas from deformation quantization are applied to expressions of elements of abstract algebras, which leads to a notion of “independence of ordering principle”. This principle is useful for the understanding of the star exponential functions and for the transcendental calculus in non-formal deformation quantization.
- Published
- 2007
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