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Title: Construction of conformally invariant higher spin operators using transvector algebras

This paper deals with a systematic construction of higher spin operators, defined as conformally invariant differential operators acting on functions on flat space R{sup m} with values in an arbitrary half-integer irreducible representation for the spin group. To be more precise, the higher spin version of the Dirac operator and associated twistor operators will be constructed as generators of a transvector algebra, hereby generalising the well-known fact that the classical Dirac operator on R{sup m} and its symbol generate the orthosymplectic Lie superalgebra osp(1,2). To do so, we will use the extremal projection operator and its relation to transvector algebras. In the second part of the article, the conformal invariance of the constructed higher spin operators will be proven explicitly.
Authors:
 [1] ;  [2]
  1. Department of Mathematics and Computer Science, University of Antwerp, Campus Middelheim, G-Building, Middelheimlaan 1, 2020 Antwerpen (Belgium)
  2. Clifford Research Group, Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Ghent (Belgium)
Publication Date:
OSTI Identifier:
22305854
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 10; Other Information: (c) 2014 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; ALGEBRA; CONFORMAL INVARIANCE; DIRAC OPERATORS; GRADED LIE GROUPS; IRREDUCIBLE REPRESENTATIONS; PROJECTION OPERATORS; SPIN