Non-linear Gauge Condition Research Articles

THE PARISI–SOURLAS MECHANISM IN YANG–MILLS THEORY?

The Parisi–Sourlas mechanism is exhibited in pure Yang–Mills theory. Using the new scalar degrees of freedom derived from the nonlinear gauge condition, we show that the nonperturbative sector of Yang–Mills theory is equivalent to a 4D O(1, 3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where [Formula: see text] is unchanged. This leads to dimensional reduction proving the equivalence of the nonperturbative sector of Yang–Mills theory to a 2D O(1, 3) sigma model.

THE CONFINEMENT MECHANISM IN YANG–MILLS THEORY?

Using the recently proposed nonlinear gauge condition [Formula: see text] we show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the nonlinear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The nonlinear sector is actually composed of "Gribov horizons" on the parallel surfaces ∂ · Aa=fa≠0. In this sector, the gauge field [Formula: see text] can be expressed in terms of fa and a new vector field [Formula: see text]. The effective dynamics of fa suggests nonperturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) fa(x) are classical solutions and averaging these solutions using a Gaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "horizons" of ∂ · Aa=fa(x) surfaces.

Solution of Nester’s gauge conditions

We give a rigorous proof of the existence of solutions to the nonlinear gauge conditions on orthonormal frames introduced by Nester to prove the positive energy theorem in general relativity. The proof holds in all dimensions n≥2. If the second de Rham cohomology group vanishes one also proves uniqueness.

Gauge fixing ambiguity and photon propagators in compact U (1) lattice gauge theory

We present the first numerical evidence of Gribov copies on a lattice. Photon propagators are numerically studied under the non-linear gauge condition ∂ μ sin θ μ = 0, where θ μ ' s are gauge potentials defined on a lattice. It is shown that this standard lattice Landau gauge condition is not unique. In the Coulomb phase a correct free propagator is obtained only after removing this ambiguity.

On the quantization of membrane theories

In connection with the quantization of membrane theories, a three-dimensional analogue of the conformal gauge is formulated on the basis of a non-linear gauge condition. The resulting action consists of polynomials in the membrane variables and Faddeev-Popov ghosts up to quartic terms, and it preserved the BRS symmetry. Some of the applications of this formulation are briefly discussed.

Renormalization of gauge theories: Non-linear gauges

The renormalization action for gauge theories quantized with non-linear gauge conditions is written down in its most general form. A natural interpretation of the well-known quartic ghost term generated by renormalization is given in terms of a generalized Faddeev-Popov determinant.

Renormalization of gauge theories with non-linear gauge conditions

It is shown that non-Abelian gauge theories can be renormalizable even when the gauge condition contains terms quadratic in field variables. When the gauge condition is non-linear, the conventional Ward-Takahashi identities are not very useful since they depend on the gauge condition explicitly. With the aid of a set of scalar fields newly introduced, the above unwanted dependence can be removed; correspondingly, the investigation into the renormalizability of gauge theories formulated in non-linear gauges is greatly simplified and is carried through in much the same way as in linear gauges. A brief discussion is also given of the renormalization of massive and massless quantum electrodynamics with non-linear gauge conditions.

Unitarity in Gauge Theories with Nonlinear Gauge Conditions

We consider the Abelian gauge theories in which the transverse and the longitudinal photons are coupled. The unitarity relation holds because the unwanted absorptive part of the amplitude due to this coupling is canceled by the fictitious particle. It is pointed out that, by introducing the Lagrange multiplier, one can see the cancellations for all orders in perturbation expansions by looking at the equation of motion for the Lagrange multiplier. The possible implication of this on the massless Yang-Mills fields is indicated.

ξ-Limiting Process in Spontaneously Broken Gauge Theories

We show that the $\ensuremath{\xi}$-limiting regularization process of Lee and Yang can be recognized as a nonlinear gauge condition in the general non-Abelian gauge theory. The $\ensuremath{\xi}$-limiting process, however, differs from the general gauge-invariant formulation of the spontaneously broken gauge theories for finite $\ensuremath{\xi}$. Some of the problems related to the implementation of general gauge conditions are also briefly discussed.