Abstract

A framework is proposed in which supersymmetries can be defined in the language of axiomatic quantum field theory. This framework contains a nuclear *-algebra into which the Borchers’ algebra of a general supermultiplet is embedded through a map which, in some sense, generalizes the concept of a superfield. The algebra of supersymmetry is represented on the constructed nuclear *-algebra as an algebra of graded derivations. Since a graded derivation cannot be integrated to a usual automorphism group (only to a formal group), it is assumed that conditions at the Lie algebraic level are strong enough to produce supersymmetric behavior. Thus it is conjectured that if a functional of the nuclear *-algebra is annihilated by the algebra of supersymmetry, and if this functional is related to a state of the Borchers’ algebra through the embedding map, this state through the GNS construction gives rise to a supersymmetric Wightman theory. This supersymmetric condition produces an infinite number of correlations among the n-point functions. The 2-point Wightman functions for a general supermultiplet are completely analyzed and it is found that their behavior is similar to the perturbative results. Finally it is proved that the free fields satisfy these supersymmetric conditions.

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