狭义相对论中量子泊松括号的变换及其物理意义  

Poisson Brackets in Four-Dimensional Vector of Special Relativity

作　　者：黄忠梅 黄伟其 HUANG Zhongmei;HUANG Weiqi(Institute of Nanophotonic Physics,College of Materials and Metallurgy,Guizhou University,Guiyang 550025,China;State Key Laboratory of Surface Physics,Key Laboratory of Micro and Nano Photonic Structures(Ministry of Education),Department of Physics,Fudan University,Shanghai 200433,China)

机构地区：[1]贵州大学材料与冶金学院,纳米光子研究所,贵州贵阳550025 [2]复旦大学物理系,表面物理国家重点实验室,上海200433

出　　处：《贵州大学学报（自然科学版）》2024年第4期15-18,共4页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金资助项目(11847084,62264002)。

摘　　要：将泊松括号从分析力学过渡到量子力学,其物理意义是很深刻的;进一步变换到狭义相对论四维时空中,其四维的量子力学泊松括号所具有的对称性和洛伦兹不变性是非常有趣的,由此给出时空光锥上四维量子力学矢量的非对易泊松括号,推导出新的物理创意和结果,探索物理量之间新的量子非对易关系。以此将量子力学与狭义相对论力学结合起来,思考近代物理中的对称性与守恒量问题,并通过非对易关系沟通物质与时空的物理图像及其联系,这些创新性工作在物理层面上具有重要的意义。In the special relativity,there is the inherent symmetry of the four-dimensional continuous domain of time and space,which is called Minkowski space.It is of great significance for classical mechanics and quantum mechanics to study the Poisson brackets of four-dimensional vector of special relativity.Classical Poisson bracket is an important operation in Hamiltonian mechanics,which is mainly used in classical mechanics and mathematics.It is more interesting that the symmetry and the Lorentz invariance of the Poisson brackets in four-dimensional vectors occur in the special relativity.We use the correspondence principle to transfer the classical Poisson bracket into the quantum form of Poisson bracket,which leads to the Heisenberg uncertainty relation.The four-dimensional Poisson brackets of special relativity in quantum mechanics will lead to some wonderful physical phenomena,in which some new uncertainty principle will be explored.

关 键 词：狭义相对论 量子泊松括号 四维量子力学矢量 量子非对易关系 

分 类 号：O412[理学—理论物理]