Null fermio-dynamics in superspace: Abelian and non-Abelian 3D massive vector fields

Abstract

Half-order actions, i.e. actions where each term contains, at most, one spinorial derivative, of all the different known 3D supersymmetric massive vector systems are given. Since the two real Grassmann coordinates ( theta 1, theta 2)= theta of the 3D superspace respectively constitute the two independent (fermionic) light-front projections of theta along the null bosonic directions x+or-=21/2 (x0-or+x1), one of them, theta 1 is regarded as the spinorial time while the other one, theta 2, is seen as a (spinorial) spacelike variable. In terms of the corresponding null spinorial timelike and spinorial spacelike derivatives the field equations contain algebraic as well as differential constraints. The authors solve them for the different known 3D vector systems and obtain their corresponding unconstrained actions in superspace. In each case their evolution is shown to be controlled by a quantity which, by analogy with the standard bosonic case, is called the superenergy of the system. The analysis of the scalar case illustrates the connection between null dynamics in superspace and the standard null dynamics in 3D bosonic spacetime. It also shows how much the superenergy contributes to the null bosonic generator of the 3D dynamics.