AI 中文总结
研究李-泊松电动力学，通过非平凡场重定义将其动力学映射到麦克斯韦理论，据此由麦克斯韦作用量对称性构造李-泊松电动力学对称性生成元和守恒流，还给出自然量子化方法。
AI 中文摘要
李-泊松电动力学（LPE）是通常电动力学的非阿贝尔且非线性变形，规范代数通过时空上的李代数型泊松括号定义。我们关注无带电物质时LPE的几何方法。建立非平凡场重定义，在温和技术假设下将LPE动力学映射到麦克斯韦理论。利用此映射，为麦克斯韦作用量的任何对称性构造LPE对称性生成元和相应守恒流。特别地，得到变形的庞加莱变换。还基于场重定义概述LPE的自然量子化方法。
英文摘要
Lie-Poisson electrodynamics (LPE) is a non-Abelian and nonlinear deformation of usual electrodynamics, where the gauge algebra is defined through a Lie-algebra-type Poisson bracket on space-time. We focus on the geometric approach to LPE in the absence of charged matter. We establish a non-trivial field redefinition which, under mild technical assumptions, maps the LPE dynamics to that of Maxwell theory. Using this map, for any symmetry of the Maxwell action, we construct generators of LPE symmetries and the corresponding conserved currents. In particular, we obtain deformed Poincaré transformations. We also outline a natural quantization prescription for LPE based on our field redefinition.
Commentsslightly extended version, submitted to a peer-reviewed journal, 15 pages
