Hamiltonian treatment of the spherically symmetric Einstein-Yang-Mills system

Journal Article · Fri Sep 10 00:00:00 EDT 1976 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(76)90074-9· OSTI ID:7240109

Cordero, P; Teitelboim, C

A canonical formalism of the dynamics of interacting spherically symmetric Yang-Mills and gravitational fields is presented. The work is based on Dirac's technique for constrained hamiltonian systems. The gauge freedom of the Yang-Mills field is treated in the same footing with the coordinate transformation freedom of the gravitational field. In particular, the fixiation of coordinates and the fixiation of the internal gauge are achieved by totally similar techniques. Two classes of spherically symmetric motions are considered: (i) the class for which the Yang-Mills potentials themselves are spherically symmetric (''manifest sphreical symmetry''). In this case the results are valid for an arbitrary gauge group; and (ii) the class for which, in the SO (3) gauge group, a rotation in physical space is compensated by a rotation of equal magnitude but opposite direction in isospin space (''spherical symmetry up to a gauge transformation''). For manifest spherical symmetry the problem amounts to effectively dealing with an abelian gauge group and the most general solution of the field equations turns out to be the Reissner-Nordstroem metric with a Coulomb field. For spherical symmetry up to a gauge transformation, the formalism contains, besides the gravitational variables, three pairs of functions of the radial coordinates that describe the degrees of freedom of the Yang-Mills field. Two pairs of these functions can be combined into a complex field psi and its conjugate. The third degree of freedom plays the role of a compensating field can always be brought to zero by a gauge transformation. After this is done the gauge is completely fixed but the problem remains invariant under position independent rotations in the psi plane. Static solutions of of the field equations in this gauge are of the form psi (r) =rho (r) EXP (ih)=0 corresponds to the Qu-Yang ansatz. A nontrivial static solution can be found in closed form.

• Research Organization: Princeton Univ., NJ
• OSTI ID: 7240109
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 100:20; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
HAMILTONIAN FUNCTION
HIGGS MODEL
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MOTION
PARTICLE MODELS
ROTATION
YANG-MILLS THEORY