Spin raising and lowering operators for Rarita-Schwinger fields

Abstract

Spin raising and lowering operators for massless field equations constructed from twistor spinors are considered. Solutions of the spin-3 2 massless Rarita-Schwinger equation from source-free Maxwell fields and twistor spinors are constructed. It is shown that this construction requires Ricci-flat backgrounds due to the gauge invariance of the massless Rarita-Schwinger equation. Constraints to construct spin raising and lowering operators for Rarita-Schwinger fields are found. Symmetry operators for Rarita-Schwinger fields via twistor spinors are obtained.

Unification of massless field equations solutions for any spin

“…Among them, Feynman and Gell-Mann dealt with a kind of prepotential for the Dirac equation [11] and Penrose [12] presented a kind of pre-potential which once integrated differs from spin to spin making it less transparent to relate solutions of different spin fields among them. There are also many other early and recent methods devised by Clebsch [13], Bateman [14], Geroch [15], Açik [16], and Bia linicky-Birula [17], to deal with solutions to field equations, for instance.…”

Harmonic spinors from twistors and potential forms

“…In an n-dimensional spin manifold M , one can define two different first-order differential operators on spinor fields. The first one is the Dirac operator defined in (19) and the second one is the Penrose operator written as follows…”

“…By using twistor spinors, the operators that transform the solutions of the massless field equations with different spin to each other can be constructed [19]. For example, a spin raising operator that takes a solution of the massless spin-0 field equation and gives a solution of the massless spin- 1 2 Dirac equation can be written in terms of twistor spinors [19,20]. This operator can also be thought as an operator that transforms the twistor spinors to harmonic spinors by using the functions that satisfiy a massless field equation.…”

Massless spin-2 fields via lower spins

“…They also appear as supersymmetry generators in superconformal field theories and conformal hidden symmetries in various backgrounds [5][6][7][8]. For massless spin- 3 2 Rarita-Schwinger fields, there is an extra tracelesness condition and the construction of spin raising and lowering operators has been done in [9]. For higher spins, especially for massless spin-2 field or graviton, more extra conditions appear and the spin raising and lowering prodecures have to be considered separately.…”