2005/11/30 by Nicolás Hatcher, N. Hatcher, A. Restuccia +1
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Hilbert space #Irreducible representation #Mathematical physics #Mathematics #Multiplet #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum mechanics #Supergravity #Superspace #Supersymmetry #Supersymmetry algebra #Tensor (intrinsic definition) #hep-th
paper · pdf · doi:10.1103/physrevd.73.046008
published as Phys.Rev.D73:046008,2006 · 20 pages;changes in the nomenclature
openalex publication_date 2006/02/24 · arxiv created 2006/03/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present the complete set of N=1, D=4 quantum algebras associated to massive superparticles. We obtain the explicit solution of these algebras realized in terms of unconstrained operators acting on the Hilbert space of superfields. These solutions are expressed using the chiral, antichiral and tensorial projectors which define the three irreducible representations of the supersymmetry on the superfields. In each case the space-time variables are noncommuting and their commutators are proportional to the internal angular momentum of the representation. The quantum algebra associated to the chiral or the antichiral projector is the one obtained by the quantization of the Casalbuoni-Brink-Schwarz (superspin 0) massive superparticle. We present a new superparticle action for the (superspin 1/2) case and show that their wave functions are the ones associated to the irreducible tensor multiplet.