Adrian TANASA
Laboratoire de Physique Theorique,
Univesit\'e of Strasbourg I,
3-5 rue de l'Universit\'e,
67084 Strasbourg cedex,
FRANCE
          and
Laboratoire de Math\'ematiques et Applications
Universit\'e de Haute Alsace
Faculté des Sciences et Techniques
4, rue des Fr\'eres Lumi\'ere
68093 Mulhouse Cedex,
FRANCE
E-mail: atanasa@lpt1.u-strasbg.fr, a.tanasa@uha.fr

Cubic supersymmetry and abelian gauge invariance

Abstract:
We consider a 4 dimensional space-time symmetry, which is a non-trivial extension of the Poincar\'e algebra. This new symmetry extract "cubic roots" of translations, hence being different from the supersymmetric extension and not contradicting the no-go theorems. Some field theoretical aspects are investigated. Boson multiplets and free Lagrangians are explicitely built. We also study in detail the interplay between this symmetry and abelian gauge symmetry.