Title
Construction of conformally invariant higher spin operators using transvector algebras Construction of conformally invariant higher spin operators using transvector algebras
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Physics
Source (journal)
Journal of mathematical physics. - New York, N.Y.
Volume/pages
55(2014) :10 , 15 p.
ISSN
0022-2488
0022-2488
Article Reference
101703
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
This paper deals with a systematic construction of higher spin operators, defined as conformally invariant differential operators acting on functions on flat space R-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 Rm 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. (C) 2014 AIP Publishing LLC.
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