Fréchet-algebraic deformation quantizations

3Quantum: Algebra Geometry Information

物理学;数学

Waldmann, S.^1

Institute for Mathematics, Julius Maximilian University Würzburg, Emil-Fischer-Straße 31, Würzburg

97074, Germany^1

关键词: Algebraic framework;    Commutation relation;    Convergence properties;    Flat phase;    Kahler manifold;    Non-trivial;    Poincare;    Star products;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/532/1/012027/pdf
DOI  :  10.1088/1742-6596/532/1/012027

来源: IOP

【 摘 要 】

In this review I present some recent results on the convergence properties of formal star products. Based on a general construction of a Fréchet topology for an algebra with countable vector space basis I discuss several examples from deformation quantization: the Wick star product on the flat phase space m2ngives a first example of a Fréchet algebraic framework for the canonical commutation relations. More interesting, the star product on the Poincare disk can be treated along the same lines, leading to a non-trivial example of a convergent star product on a curved Kahler manifold.