星积与几何代数
Star Products and Geometric Algebra
摘要：
几何代数的形式可以描述为变形超分析。变形是用一个费米子星积完成的，它来自于伪经典力学的变形量子化。如果我们把变形扩展到超分析的玻色子系数部分，我们就得到了有自旋系统的量子力学。这种方法一方面阐明了几何代数中Grassmann结构与Clifford结构之间的关系，另一方面阐明了经典力学与量子力学之间的关系。此外，它给出了一个形式主义，允许处理经典和量子力学在一个一致的方式。
英文摘要：
The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the deformation to the bosonic coefficient part of superanalysis one obtains quantum mechanics for systems with spin. This approach clarifies on the one hand the relation between Grassmann and Clifford structures in geometric algebra and on the other hand the relation between classical mechanics and quantum mechanics. Moreover it gives a formalism that allows to handle classical and quantum mechanics in a consistent manner.
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。
