Causal algebra and its applications to physics
Causal algebra and its applications to physics
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因果代数及其在物理学中的应用
DOI：
10.7498/aps.60.020201
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发表时间：
2011-02
期刊：
影响因子：
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通讯作者：
Song Jia-Min
中科院分区：
文献类型：
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作者：
Huang Yong-Chang;Huang Chang-Yu;Yang Shi-Lin;He Bin;Song Jia-Min
提出了一种因果代数及其在高能物理中的应用。首先，在定量因果原理的基础上，提出了因果代数和因果分解代数。利用因果分解代数推导出结合律和单位式，并推断因果分解代数自然包含群的结构。最后给出了新代数系统在高能物理中的应用。我们发现既不属于群也不属于环的高能粒子的反应，因果代数和因果分解代数是精确描述粒子物理中真实的反应的严格工具。得到了不同粒子间不同量相互作用的一般统一表达式（具有乘性或加性）。利用因果代数的表示和超对称R数，得到了含有超对称粒子的反应的乘性的超对称PR =（-1）R不变性.此外，还得到了电子自旋各分量之间的对称关系，从而简化了多电子相互作用的计算。利用互逆可消条件定义广义逆元，可以更新群的定义，并通过消除一个多余的定义使群的公理数目减少到3个。
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 P R =(-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.