Canonical formulation of the self-dual Yang-Mills system : algebras and hierarchies

We construct a canonical formulation of the self-dual Yang-Mills system formulated in the gauge-invariant group-valued {ital J} fields and derive their Hamiltonian and the quadratic algebras of the fundamental Dirac brackets. We also show that the quadratic algebras satisfy Jacobi identities and the...

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Bibliographic Details
Published in:Physical review letters 1992-03, Vol.68 (12), p.1807-1810
Main Authors: CHAU, L.-L, YAMANAKA, I
Format: Article
Language:English
Subjects:
ALGEBRA
Classical and quantum physics: mechanics and fields
Exact sciences and technology
HAMILTONIANS
MATHEMATICAL OPERATORS
MATHEMATICS
NONLINEAR PROBLEMS
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Quantum mechanics
QUANTUM OPERATORS 662110 > General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
SYMMETRY
YANG-MILLS THEORY
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Summary:We construct a canonical formulation of the self-dual Yang-Mills system formulated in the gauge-invariant group-valued {ital J} fields and derive their Hamiltonian and the quadratic algebras of the fundamental Dirac brackets. We also show that the quadratic algebras satisfy Jacobi identities and their structure matrices satisfy modified Yang-Baxter equations. From these quadratic algebras, we construct Kac-Moody-like and Virasoro-like algebras. We also discuss their related symmetries, involutive conserved quantities, and hierarchies of nonlinear and linear equations.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.68.1807