An exact one monopole solution in a uniform self-dual background field is obtained in the BPS limit of the SU(2) Yang-Mills-Higgs theory by using the inverse scattering method.

We discuss the possible form of gluon and ghost propagators in the infrared region of Yang-Mills theory in the covariant gauge from the viewpoint of general principles of quantized gauge field theories.

The damping rate of a Higgs field at zero momentum is calculated using the Braaten-Pisarski method and compared to the Lyapunov exponent of the classical SU(2) Yang-Mills Higgs system.

It is shown that in the SU(2) Yang Mills Higgs theory with broken gauge symmetry a flux tube solution filled with a color longitudinal electric field exists. The origin of the gauge symmetry breakdown for this case is discussed.

A nonlinear vector supersymmetry for three-dimensional topolog-ical massive Yang-Mills is obtained by making use of a nonlinear but local and covariant redefinition of the gauge field.

The Bianchi equations are determined for the deformed spinor bundle S̃M = SM × R. Also, the Yang-Mills-Higgs equations are derived, and a geometrical interpretation of the Higgs field is given. Mathematics Subject Classification: 81R25, 81T13, 53B30, 81T20, 53B50

Two classes of observables defined on the configuration space of a particle are quantized, and the effects of the Yang-Mills field are discussed in the context of geometric quantization.

A cutoff regularization for a pure Yang-Mills theory is implemented within the background field method keeping explicit the gauge invariance of the effective action. The method has been applied to compute the beta function at one loop order.

We establish the existence of hairy black holes in su(N) Einstein-Yang-Mills theories, described by N − 1 parameters, corresponding to the nodes of the gauge field functions.

It is shown that static purely electric or purely magnetic abelian field configurations in Yang-Mills theory are unstable when the electric or magnetic field strength is too large over too wide a region. The critical parameter is gEL2 (gBL2) where E (B) is a measure of the field strength, and L is a measure of the distance over which such field strengths extend.