Spinor formalism for massive fields with half-integral spin

TL;DR

This paper extends the spinor formalism to describe massive fields with half-integer spins, enabling explicit calculation of helicity amplitudes and three-particle vertices, and revealing near-massless-like gauge restrictions.

Contribution

It introduces a spinor-based method for massive half-integer spin fields, generalizing previous massless formalisms and providing explicit amplitude expressions for higher helicities.

Findings

Explicit spinor forms for massive fields of any spin and helicity.

Extension of three-particle vertex expressions to massive particles.

Restrictions from gauge and Lorentz invariance are similar to the massless case.

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.