Discrete quantum modes of the Dirac field in AdSd+1 backgrounds
Abstract
It is shown that the free Dirac equation in spherically symmetric static backgrounds of any dimensions can be put in a simple form using a special version of Cartesian gauge in Cartesian coordinates. This is manifestly covariant under the transformations of the isometry group so that the generalized spherical coordinates can be separated in terms of angular spinors like in the flat case, obtaining a pair of radial equations. In this approach the equation of the free field Dirac in AdSd+1 backgrounds is analytically solved obtaining the formula of the energy levels and the corresponding normalized eigenspinors.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.