作者：Akira Yoshioka 来源：[C].Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization2018Project Euclid 摘要：We introduce star products for certain function space containing polynomials, and then we obtain an associative algebra of functions. In this algebra we can consider exponential elements, which are called star exponentials. Using star exponentials we can define star functions in ...
 作者：Kiyonori Hosokawa , Tsukasa Takeuchi , Akira Yoshioka 来源：[C].Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization2018Project Euclid 摘要：Symplectic-Haantjes manifolds are constructed for several Hamiltonian systems following Tempesta-Tondo [5], which yields the complete integrability of systems.
 作者：Akira Yoshioka , Tomoyo Kanazawa 来源：[C].Proceedings of the Sixteenth International Conference on Geometry, Integrability and Quantization2015Project Euclid 摘要：We give a review on non formal star product and its star exponentials with concrete examples.
 作者：Akira Yoshioka , Tomoyo Kanazawa 来源：[C].Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization2016Project Euclid 摘要：We give a brief review on Weyl manifold as a quantization of symplectic manifold, equipped with a system of quantized canonical charts and quantized canonical transformations among them called Weyl diffeomorphism. Weyl manifold is deeply related to deformation quantization on sym...
 作者：Tomoyo Kanazawa , Akira Yoshioka 来源：[C].Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization2014Project Euclid 摘要：Starting from the Moyal product on eight-dimensional canonicalEuclidean phase space $T^* \mathbb{R}^4$ with an $S^1$-symplecticaction, we construct a non-formal star product, i.e., thedeformation parameter is a real number, on the cotangent bundle ofthree-dimensional Euclidean sp...
 作者：Akira Yoshioka , Toshio Matsumoto 来源：[C].Proceedings of the Fourth International Conference on Geometry, Integrability and Quantization2003Project Euclid 摘要：The Moyal product is considered on the complex plane $\mathbb{C}^2$. Path integral representation of $\ast$-exponential function is given for a quadratic form on $\mathbb{C}^2, H = ax^2 + 2bxy +cy^2$ for $(x,y) \in \mathbb{C}^2$, where $a,b,c \in \mathbb{C}$.
 作者：Tomoyo Kanazawa , Akira Yoshioka 来源：[C].Proceedings of the Thirteenth International Conference on Geometry, Integrability and Quantization2012Project Euclid 摘要：We show that the MIC-Kepler probrem is simply solved via the phase-space formulation of non-relativistic quantum mechanics. The MIC-Kepler problem is the Hamiltonian system behind the hydrogen atom subjected to the influence of the Dirac’s magnetic monopole field and the squ...
 作者：Mari Iida , Akira Yoshioka 来源：[C].Proceedings of the Twelfth International Conference on Geometry, Integrability and Quantization2011Project Euclid 摘要：A family of star products parametrized by complex matrices is defined. Especially commutative associative star products are treated, and star exponentials with respect to these star products are considered. Jacobi's theta functions are given as infinite sums of star exponentials....
 作者：Toshio Tomihisa , Akira Yoshioka 来源：[C].Proceedings of the Eleventh International Conference on Geometry, Integrability and Quantization2010Project Euclid 摘要：Here we extend the star products by means of complex symmetric matrices. In this way we obtain a family of star products. Next we consider the star exponentials with respect to these star products, and finally we obtain several interesting identities.