Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 004, 17 pages      arXiv:0801.1892      https://doi.org/10.3842/SIGMA.2008.004
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Generalized Symmetries of Massless Free Fields on Minkowski Space

Juha Pohjanpelto a and Stephen C. Anco b
a) Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605, USA
b) Department of Mathematics, Brock University, St. Catharines ON L2S 3A1 Canada

Received November 01, 2007; Published online January 12, 2008

Abstract
A complete and explicit classification of generalized, or local, symmetries of massless free fields of spin s ≥ 1/2 is carried out. Up to equivalence, these are found to consists of the conformal symmetries and their duals, new chiral symmetries of order 2s, and their higher-order extensions obtained by Lie differentiation with respect to conformal Killing vectors. In particular, the results yield a complete classification of generalized symmetries of the Dirac-Weyl neutrino equation, Maxwell's equations, and the linearized gravity equations.

Key words: generalized symmetries; massless free field; spinor field.

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