On the Velo-Zwanziger phenomenon
J. Frauendiener
TL;DR
This paper investigates the consistency of the Rarita-Schwinger equation in curved spacetime with electromagnetic fields, finding it only consistent on Einstein manifolds without electromagnetic influence.
Contribution
It derives Buchdahl conditions for the Rarita-Schwinger equation in a 2-component spinor formalism, revealing limitations on background geometries and fields.
Findings
Equation consistent only on Einstein manifolds with no electromagnetic field
Derivation of Buchdahl conditions for the Rarita-Schwinger equation
Analysis in 2-component spinor formalism
Abstract
The Rarita-Schwinger equation in a curved background and an external electromagnetic field is discussed. We analyse the equation in the 2-component spinor formalism and derive Buchdahl conditions for them. The result is that the equation can consistently be imposed only on Einstein manifolds with vanishing electromagnetic field.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Geometry Research · Algebraic and Geometric Analysis