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摘要
This paper gives a generalization of group theory, i.e. a unification theory of different causal algebras, and its applications to theoretical physics. We propose left and right causal algebras, left and right causal decomposition algebras, causal algebra and causal decomposition algebras in terms of quantitative causal principle. The causal algebraic system of containing left (or right) identity I(jL) (or I(jR)) is called as the left (or right) causal algebra, and associative law is deduced. Furthermore the applications of the new algebraic systems are given in theoretical physics, specially in the reactions of containing supersymmetric particles, we generally obtain the invariance of supersymmetric parity of multiplying property. In the reactions of particles of high energy, there may be no identity, but there are special inverse elements, which make that the relative algebra be not group, however, the causal algebra given in this paper is just a tool of severely and directly describing the real reactions of particle physics. And it is deduced that the causal decomposition algebra is equivalent to group.
