Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

Journal Article · Wed Apr 15 00:00:00 EDT 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3104066· OSTI ID:21294028

Barnich, Glenn; Troessaert, Cedric ^[1]

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1. Physique Theorique et Mathematique, Universite Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium)

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity, and massless higher spin gauge fields.

• OSTI ID: 21294028
• Journal Information: Journal of Mathematical Physics, Vol. 50, Issue 4; Other Information: DOI: 10.1063/1.3104066; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DUALITY
ELECTROMAGNETISM
GRAVITATION
HAMILTONIANS
INTEGRAL EQUATIONS
MATHEMATICAL EVOLUTION
MAXWELL EQUATIONS
PHASE SPACE
POISSON EQUATION
SPIN
YANG-MILLS THEORY