Canonical formulation of the spherically symmetric Einstein--Yang--Mills--Higgs system for a general gauge group

Journal Article · Thu Sep 01 00:00:00 EDT 1977 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(77)90352-9· OSTI ID:5296978

Cordero, P

The dynamics of the spherically symmetric system of gravitation interacting with scalar and Yang--Mills fields is presented in the context of the canonical formalism. The gauge group considered is a general (compact and semisimple) N parameter group. The scalar (Higgs) field transforms according to an unspecified M-dimensional orthogonal representation of the gauge group. The canonical formalism is based on Dirac's techniques for dealing with constrained hamiltonian systems. First the condition that the scalar and Yang--Mills fields and their conjugate momenta be spherically symmetric up to a gauge is formulated and solved for global gauge transformations, finding, in a general gauge, the explicit angular dependence of the fields and conjugate momenta. It is shown that if the gauge group does not admit a subgroup (locally) isomorphic to the rotation group, then the dynamical variables can only be manifestly spherically symmetric. If the opposite is the case, then the number of allowed degrees of freedom is connected to the angular momentum content of the adjoint representation of the gauge group. Once the suitable variables with explicit angular dependence have been obtained, a reduced action is derived by integrating away the angular coordinates. The canonical formulation of the problem is now based on dynamical variables depending only on an arbitrary radial coordinate r and an arbitrary time coordinate t. Besides the gravitational variables, the formalism now contains two pairs of N-vector variables, (R, ..pi../sub R/), (THETA, ..pi../sub Theta)/corresponding to the allowed Yang--Mills degrees of freedom and one pair of M-vector variables, (h, ..pi../sub h/), associated with the original scalar field. The reduced Hamiltonian is invariant under a group of r-dependent gauge transformations such that R plays the role of the gauge field (transforming in the typically inhomogeneous way) and in terms of which the gauge covariant derivatives of THETA and h naturally appear.

• Research Organization: International Centre for Theoretical Physics, Trieste, Italy
• OSTI ID: 5296978
• Journal Information: Ann. Phys. (N.Y.); (United States), Vol. 108:1
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
GRAVITATIONAL INTERACTIONS
YANG-MILLS THEORY
GAUGE INVARIANCE
HIGGS MODEL
SCALAR FIELDS
SO-3 GROUPS
SYMMETRY BREAKING
BASIC INTERACTIONS
INTERACTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE MODELS
SO GROUPS
SYMMETRY GROUPS
645400* - High Energy Physics- Field Theory