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This paper shows that the formal Grassmann multiplication rules used for manipulating the tetrad and spin-3/2 field in classical supergravity theory can be replaced by new rules under which the spin-3/2 field is not anticommuting (or commuting). Supersymmetry invariance of the theory is maintained at the cost of adding some new terms to the usual Majorana form for the action and the supersymmetry transformation of the fields. The new terms change sign under parity reversal, so the supersymmetry does not commute with parity transformations, and the coupling of the spin-3/2 field to the tetrad is not parity invariant. (These features are closely tied to an equivalent chiral formation for the theory, where the spin-3/2 field is left handed rather than Majorana.) The mathematical structure of the new rules is based on a novel multiplication that lacks the graded commutativity and associativity built in for products of the supergravity fields under Grassmann multiplication.
Physical Review D – American Physical Society (APS)
Published: Aug 15, 1994
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