### Abstract

We propose suitable ideas for non-formal deformation quantization of Fréchet Poisson algebras. To deal with the convergence problem of deformation quantization, we employ Fréchet 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.

Original language | English |
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Pages (from-to) | 153-175 |

Number of pages | 23 |

Journal | Letters in Mathematical Physics |

Volume | 82 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 2007 Dec |

### Fingerprint

### Keywords

- Independence of ordering principle
- Non-formal deformation quantization
- Star exponential functions
- Symbol calculus

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*,

*82*(2-3), 153-175. https://doi.org/10.1007/s11005-007-0208-5

**Orderings and non-formal deformation quantization.** / Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 82, no. 2-3, pp. 153-175. https://doi.org/10.1007/s11005-007-0208-5

}

TY - JOUR

T1 - Orderings and non-formal deformation quantization

AU - Omori, Hideki

AU - Maeda, Yoshiaki

AU - Miyazaki, Naoya

AU - Yoshioka, Akira

PY - 2007/12

Y1 - 2007/12

N2 - We propose suitable ideas for non-formal deformation quantization of Fréchet Poisson algebras. To deal with the convergence problem of deformation quantization, we employ Fréchet 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.

AB - We propose suitable ideas for non-formal deformation quantization of Fréchet Poisson algebras. To deal with the convergence problem of deformation quantization, we employ Fréchet 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.

KW - Independence of ordering principle

KW - Non-formal deformation quantization

KW - Star exponential functions

KW - Symbol calculus

UR - http://www.scopus.com/inward/record.url?scp=37049013346&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37049013346&partnerID=8YFLogxK

U2 - 10.1007/s11005-007-0208-5

DO - 10.1007/s11005-007-0208-5

M3 - Article

VL - 82

SP - 153

EP - 175

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 2-3

ER -