Spinor formalism for massive fields with half-integral spin

Abstract

In this article, we extend the %Weyl-van der Waerden spinor technique for calculating helicity amplitudes to general massive fields of half-integer spins. We find that the little group generators can be represented as first-order differential operators in the spinor formalism. We use the spinor forms of the generators to get the explicit form of the massive fields of any spin and any helicity. We also deal with the three-particle S-matrix by these spinor form generators, and find that we are able to extend the explicit form of the three-particle vertex obtained by Benincasa and Cachazo to the massive case. We present the explicit expressions for the amplitudes with external particles of the lowest helicities up to -3/2. Group theory, in the form of raising operators of the little group, then dictates other amplitudes with higher helicity in the same spin multiplets. The formalism allows, in principle, to determine the electromagnetic form-factors of charged particles of arbitrary helicities, without additional assumptions about the underlying lagrangian. We find that restrictions which follow from gauge and Lorentz invariance are nearly as restrictive as in the massless case.