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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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