Supersymmetry: superfield equations of motion

Abstract

Abstract. Supersymmetry and superfields are considered in connection with Poincaré superalgebras. A formalism of projection operators for deriving wave equations for ordinary fields and superfields is developed. Superfield equations of motion in the case of massive and massless fields are presented together with an application in linear supergravity.1. Supersymmetry, superfields, Poincaré superalgebra Supersymmetry has been known more than few decades, but it is still alive despite the absence of experimental verification. Supersymmetry offers several relevant theoretical solutions for modern physics. Supersymmetry (Bose-Fermi symmetry)Let us consider a general N = 1 superfieldwhere θ α is a four-component anticommuting Majorana spinor and i is a Lorentz index. Now we introduce the most general Poincaré superalgebra [1]. The generators of the Poincaré group P µ and M µν , and n supergenerators S α (α = 1, 2, . . . , n) satisfy the following relations:where η µν = diag(+ ---). The simple N = 1 supersymmetry algebra is related to the bispinor representation of the Lorentz group. We have four bispinor generators S α , B µν = 1 2 σ µν and A µ = γ µ C. The Nextended Poincaré superalgebra is related to the direct sum of N bispinor representations. New possibilities [2]• In the most general case the matrices A µ are related to the β-matrices of an invariant first order wave equation