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Orderings and Non-formal Deformation Quantization

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Science University of Tokyo, Noda, Chiba, 278-8510, Japan

    Hideki Omori

  2. Department of Mathematics, Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama, 223-8522, Japan

    Yoshiaki Maeda

  3. Department of Mathematics, Faculty of Economics, Keio University, Hiyoshi, Yokohama, 223-8521, Japan

    Naoya Miyazaki

  4. Department of Mathematics, Faculty of Science, Science University of Tokyo, Kagurazaka, Tokyo, 102-8601, Japan

    Akira Yoshioka

Authors
  1. Hideki Omori
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  2. Yoshiaki Maeda
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  3. Naoya Miyazaki
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  4. Akira Yoshioka
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Correspondence to Yoshiaki Maeda.

Additional information

Yoshiaki Maeda was partially supported by Grant-in-Aid for Scientific Research (#18204006.), Ministry of Education, Science and Culture, Japan.

Naoya Miyazaki was partially supported by Grant-in-Aid for Scientific Research (#18540093.), Ministry of Education, Science and Culture, Japan.

Akira Yoshioka was partially supported by Grant-in-Aid for Scientific Research (#19540103.), Ministry of Education, Science and Culture, Japan.

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Omori, H., Maeda, Y., Miyazaki, N. et al. Orderings and Non-formal Deformation Quantization. Lett Math Phys 82, 153–175 (2007). https://doi.org/10.1007/s11005-007-0208-5

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  • DOI: https://doi.org/10.1007/s11005-007-0208-5

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