因果代数及其在物理学中的应用  

Causal algebra and its applications to physics

作　　者：黄永畅[1] 何斌[1,2] 黄昌宇[3] 杨士林[2] 宋加民[1] 

机构地区：[1]北京工业大学理论物理研究所,北京100124 [2]北京工业大学应用数学研究所,北京100124 [3]北京大学物理学院,北京100871

出　　处：《物理学报》2011年第2期1-9,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10875009;11072007);北京市自然科学基金(批准号:1072005;1082002)资助的课题~~

摘　　要：依据定量因果原理,给出了物理学中的一个因果代数的应用,当满足定量因果原理的互逆可消条件且又满足消去律的解时,得到因果分解代数;由因果分解代数导出了结合律和单位元,进而导出了因果分解代数又具有群的结构特征,同时给出了这新代数系统在高能物理学中的应用.严格地给出了在高能物理中既不是群又不是环的反应,发现因果代数和因果分解代数是严格描述粒子物理反应的基本工具,得到了所有各种相加性、相乘性物理量和各种粒子反应都必须满足的统一恒等式,给出了因果代数和因果分解代数对高能物理的具体应用.利用因果代数的表示和超对称的R数,得到了含有超对称粒子反应中相乘性的超对称的PR=(-1)R对称性.还得到了一个关于电子自旋角动量的任意分量间的一个对称关系式,利用这对称关系式,可以化简多电子相互作用的计算.利用互逆可消条件定义了一般的逆元,可重新定义群,使群的公理减少一个,消除了重复定义.A causal algebra and its application to high energy physics is proposed. Firstly on the basis of quantitative causal principle,we propose both a causal algebra and a causal decomposition algebra. Using the causal decomposition algebra, the associative law and the identity are deduced,and it is inferred that the causal decomposition algebra naturally contains the structures of group. Furthermore,the applications of the new algebraic systems are given in high energy physics. We find that the reactions of particles of high energy belonging neither to the group nor to the ring,and the causal algebra and the causal decomposition algebra are rigorous tools exactly describing real reactions of particle physics. A general unified expression （ with multiplicative or additive property） of different quantities of interactions between different particles is obtained. Using the representation of the causal algebra and supersymmetric R number,the supersymmetric PR = （-1 ） R invariance of multiplying property in the reactions of containing supersymmetric particles is obtained. Furthermore,a symmetric relation between any components of electronic spin is obtained,with the help of which one can simplify the calculation of interactions of many electrons. The reciprocal eliminable condition to define general inverse elements is used,which may renew the definition of the group and make the number of axioms of group reduced to three by eliminating a superabundant definition.

关 键 词：对称性 群论 因果原理 粒子物理 

分 类 号：O572.2[理学—粒子物理与原子核物理]