Abstract
Spin raising and lowering operators for massless field equations constructed from twistor spinors are considered. Solutions of the spin-$\frac{3}{2}$ 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.
Highlights
In four dimensional conformally flat spacetimes, the solutions of the massless field equations for different spins can be mapped to each other by spin raising and lowering procedures [1]
A spin raising operator is an operator constructed from a twistor spinor and gives a solution of the spin-(s þ 12) massless field equation from a solution of the spin-s massless field equation
Twistor spinors are special spinors defined as the solutions of the twistor equation on a spin manifold
Summary
In four dimensional conformally flat spacetimes, the solutions of the massless field equations for different spins can be mapped to each other by spin raising and lowering procedures [1]. Rarita-Schwinger fields appear as sources of torsion and curvature in supergravity field equations They correspond to spinor-valued 1-forms that are in the kernel of the Rarita-Schwinger operator which can be seen as the generalization of the Dirac operator to spin-32 fields. Spin raising and lowering procedures can allow us to find the solutions of the massless RaritaSchwinger equation by using spin-1 source-free Maxwell solutions and twistor spinors. We focus on the construction of spin raising, spin lowering, and symmetry operators for massless RaritaSchwinger fields. Spin lowering operators are constructed for four dimensional fields and a constraint relating the Rarita-Schwinger field with the curvature characteristics of the background is found. We construct a symmetry operator for Rarita-Schwinger fields by using spin raising and lowering operators which map a solution of the massless Rarita-Schwinger equation to another solution. We give the transformation rules between the languages of Clifford calculus and gamma matrices to write the equalities in the paper in an alternative notation
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