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Lagrangian gauge theories on supermanifolds

  • Ugo Bruzzo
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1251)

Abstract

We describe an approach to the formulation of superspace supersysmmetric field theories based on the theory of supermanifolds (in the sense of DeWitt-Rogers). As a first step, we set up a variational calculus on fibered supermanifolds. Suitable definitions of the properties of local gauge and general invariance of a supermanifold field theory are given and equivalence of these invariances to generalizations of Utiyama theorem is proved. We show that, under some conditions, the extremality of the action functional is locally equivalent to a set of differential equations on the supermanifold.

Another main point in this article is the generalization of Noether theorem to supermanifold field theory. It is indeed shown that the above mentioned invariances are equivalent to a pair of differential identities (strong conservation laws).

The paper ends with the discussion of an example, namely, superspace N=1 supergravity.

Keywords

Local Injection General Invariance Variational Calculus Superspace Formulation Supersymmetric Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Ugo Bruzzo
    • 1
  1. 1.Dipartimento di MatematicaUniversita' di GenovaGenovaItaly

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