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Title: Induced representations of tensors and spinors of any rank in the Stueckelberg-Horwitz-Piron theory

We show that a modification of Wigner’s induced representation for the description of a relativistic particle with spin can be used to construct spinors and tensors of arbitrary rank, with invariant decomposition over angular momentum. In particular, scalar and vector fields, as well as the representations of their transformations, are constructed. The method that is developed here admits the construction of wave packets and states of a many body relativistic system with definite total angular momentum. Furthermore, a Pauli-Lubanski operator is constructed on the orbit of the induced representation which provides a Casimir operator for the Poincaré group and which contains the physical intrinsic angular momentum of the particle covariantly.
Authors:
 [1] ;  [2] ;  [2] ;  [1]
  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University, Ramat Aviv, Tel Aviv 69978 (Israel)
  2. (Israel)
Publication Date:
OSTI Identifier:
22479600
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CASIMIR OPERATORS; MANY-BODY PROBLEM; MODIFICATIONS; ORBITS; RELATIVISTIC RANGE; SCALARS; SPIN; SPINORS; TENSORS; VECTOR FIELDS