
SIGMA 4 (2008), 004, 17 pages arXiv:0801.1892
http://dx.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 973314605, 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 higherorder
extensions obtained by Lie differentiation
with respect to conformal Killing vectors.
In particular, the results yield a complete classification
of generalized symmetries of the DiracWeyl neutrino equation,
Maxwell's equations, and the linearized gravity equations.
Key words:
generalized symmetries; massless free field; spinor field.
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