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.