Cubic supersymmetry and abelian gauge invariance

On the basis of recent results extending non-trivially the Poincaré symmetry, we investigate the properties of bosonic multiplets including 2−form gauge fields. Invariant free Lagrangians are explicitly built which involve possibly 3− and 4−form fields. We also study in detail the interplay between this symmetry and a U(1) gauge symmetry, and in particular the implications of the automatic gauge-fixing of the latter associated to a residual gauge invariance, as well as the absence of self-interaction terms. PACS numbers: 03.50.Kk, 03.65.Fd, 11.30.Ly keywords: extensions of the Poincaré algebra, Field Theory, algebraic methods, Lie (super)algebras, gauge symmetry. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]