Spin-1/2 and spin-3/2 field solutions in plane wave spacetimes

TL;DR

This paper presents explicit solutions for massless Dirac and massive Rarita-Schwinger fields in plane wave spacetimes, including symmetry operators and bilinear relations, highlighting the structure of spinor fields in such backgrounds.

Contribution

It provides new explicit solutions for spin-1/2 and spin-3/2 fields in plane wave spacetimes, along with symmetry operators and algebraic relations, advancing understanding of fermionic fields in curved backgrounds.

Findings

Found two massless Dirac solutions and two massive Rarita-Schwinger solutions.

Constructed a symmetry operator transforming one Dirac solution into another.

Identified the spinor bilinear structure and algebraic relations in the solutions.

Abstract

We have found two non-trivial massless Dirac and two massive Rarita-Schwinger solutions in plane wave spacetimes. The first order symmetry operator transforming one of the massless Dirac solution to the other is constructed. The only non-vanishing spinor bilinear generated by the standard spinor basis is obtained and algebraic relations between the induced parallel forms are demonstrated. It is also seen that the spin-3/2 norm of the Rarita-Schwinger solutions enforces to the massless sector.