Tensors and spinors in de Sitter space
Ben Pethybridge, Vladimir Schaub
Abstract
A bstract We construct the Wightman function for symmetric traceless tensors and Dirac fermions in dS d +1 in a coordinate and index free formalism using a d + 2 dimensional ambient space. We expand the embedding space formalism to cover spinor and tensor fields in any even or odd dimension. Our goal is to furnish a self-contained toolkit for the study of fields of arbitrary spin in de Sitter, with applications to cosmological perturbation theory. The construction for spinors is shown in extensive detail. Concise expressions for the action of isometry generators on generic bulk fields, the 2-point function of bulk spinors, and a derivation of the uplift of the spinorial covariant derivative are included.
Topics & Concepts
SpinorMathematical physicsCovariant transformationDe Sitter spacePhysicsAnti-de Sitter spaceAmbient spaceDe Sitter universeMathematicsQuantum mechanicsPure mathematicsUniverseBlack Holes and Theoretical PhysicsCosmology and Gravitation TheoriesParticle physics theoretical and experimental studies