2020/09/30 by Lorenzo Iacobacci, Wolfgang Mück · 37 citations
Mathematics · Physics and Astronomy · #Basis (linear algebra) #Black Holes and Theoretical Physics #Conformal map #Cosmology and Gravitation Theories #Dirac (video compression format) #Dirac algebra #Dirac equation #Gamma matrices #Geometry #Lorentz transformation #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Space (punctuation) #Spinor #Wave function #hep-th
paper · pdf · doi:10.1103/physrevd.102.106025
published in Physical review. D/Physical review. D. 102(10) (American Physical Society) · 21 pages, v2: added references, v3: added calculation of the explicit form of the wave function
arxiv created 2020/11/18 · openalex publication_date 2020/11/24 · arxiv updated 2020/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study solutions to the Dirac equation in Minkowski space ℝ1,d+1 that transform as d-dimensional conformal primary spinors under the Lorentz group SO(1,d+1). Such solutions are parametrized by a point in ℝd and a conformal dimension \mathrm\ensuremathΔ. The set of wave functions that belong to the principal continuous series, \mathrm\ensuremathΔ=(d)/(2)+i\ensuremathν, with \ensuremathν\ensuremath≥0 and \ensuremathν\ensuremath∈ℝ in the massive and massless cases, respectively, form a complete basis of delta-function normalizable solutions of the Dirac equation. In the massless case, the conformal primary wave functions are related to the wave functions in momentum space by a Mellin transform.