量子磁代数与磁曲率
Quantum Magnetic Algebra and Magnetic Curvature
摘要：
与带电粒子相关联的相空间的辛几何是通过将法拉第2-形式添加到欧几里得相空间上的标准结构来确定的。本文描述了满足非线性对易关系的坐标和动量算符中Weyl对称化函数的相应代数。这个代数中的乘法生成相空间上函数的结合积。这个乘积由积分核给出，积分核的相位是群胚相容膜的辛面积。从与Stratonovich量化器相关联的磁反射中提取具有非平凡曲率的辛相空间连接。零曲率和常曲率的情况下被认为是作为例子。得到了静态和含时电磁场的量子化。膨胀的产品的变形参数，写在协变的形式，与已知的变形量子化公式进行比较。
英文摘要：
The symplectic geometry of the phase space associated with a charged particle is determined by the addition of the Faraday 2-form to the standard structure on the Euclidean phase space. In this paper we describe the corresponding algebra of Weyl-symmetrized functions in coordinate and momentum operators satisfying nonlinear commutation relations. The multiplication in this algebra generates an associative product of functions on the phase space. This product is given by an integral kernel whose phase is the symplectic area of a groupoid-consistent membrane. A symplectic phase space connection with non-trivial curvature is extracted from the magnetic reflections associated with the Stratonovich quantizer. Zero and constant curvature cases are considered as examples. The quantization with both static and time dependent electromagnetic fields is obtained. The expansion of the product by the deformation parameter, written in the covariant form, is compared with the known deformation quantization formulas.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
