Causal algebra and its applications to physics

Abstract

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.