Abstract
We attempt to establish a calculus of the Moyal product treating the deformation parameter as a parameter moving in positive reals. We show strange phenomenas different from formal deformation quantization by studying the convergence of the parameter in computing the product of the exponential functions of the quadratic form. In the case of deformation quantization with the positive real parameters, the associativity for the Moyal product fails for a wider class of functions.
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References
F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Stemheimer Deformation theory and quantization I, Ann. Phs. 111 (1978)61–110.
D. Deligne, Déformation de l’algèbre des fonctions dúne variété symplectique, Select Math. New series 1, 1995.
Japanese Math. Soc. Encyclopedia of mathematics, Iwanami, 1985.
M. Kontsevich, Deformation quantization of Poisson manifold I, q-alg/9709040.
R. Kolchin, On the Galois theory of differential fields, Amer. J. Math., 77 (1955)868–894.
M. Morimoto, An introduction to Sato’s hyperfunctions, AMS Trans. Mono. 129, 1993.
H. Omori, Infinite dimensional Lie groups, AMS Trans. Mono., 158, 1997.
H. Omori, Y. Maeda, A. Yoshioka, Weyl manifolds and deformation quantization, Adv. Math, vol 85, No 2, 224-255, 1991
H. Omori, Y. Maeda, N. Miyazaki, A. Yoshioka, Anomalous exponent for convergent star-product on Fréchet-Poisson algebras, preprint.
B. de Witt, Supermanifolds, Cambridge Univ. Press, 1984
K. Yoshida, Functional analysis, Springer 1966.
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© 2001 Springer Science+Business Media Dordrecht
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Omori, H., Maeda, Y., Miyazaki, N., Yoshioka, A. (2001). Singular Systems of Exponential Functions. In: Maeda, Y., Moriyoshi, H., Omori, H., Sternheimer, D., Tate, T., Watamura, S. (eds) Noncommutative Differential Geometry and Its Applications to Physics. Mathematical Physics Studies, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0704-7_11
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DOI: https://doi.org/10.1007/978-94-010-0704-7_11
Publisher Name: Springer, Dordrecht
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