The Most General and Renormalizable Maximal Abelian Gauge

Abstract

We construct the most general gauge fixing and the associated Faddeev-Popov ghost term for the SU(2) Yang-Mills theory, which leaves the global U(1) gauge symmetry intact (i.e., the most general Maximal Abelian gauge). We show that the most general form involves eleven independent gauge parameters. Then we require various symmetries which help to reduce the number of independent parameters for obtaining the simpler form. In the simplest case, the off-diagonal part of the gauge fixing term obtained in this way is identical to the modified maximal Abelian gauge term with two gauge parameters which was proposed in the previous paper from the viewpoint of renormalizability. In this case, moreover, we calculate the beta function, anomalous dimensions of all fields and renormalization group functions of all gauge parameters in perturbation theory to one-loop order. We also discuss the implication of these results to obtain information on low-energy physics of QCD.

24 pages, 3 figures

References in corpus (4)

• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Abelian dominance in low-energy Gluodynamics due to dynamical mass generation
• Renormalizable Abelian-projected effective gauge theory derived from Quantum Chromodynamics
• Renormalizable Abelian-projected effective gauge theory derived from Quantum Chromodynamics II

Cited by in corpus (18)

• The Gribov problem and QCD dynamics
• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• An analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge
• Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum
• Infrared Saturation and Phases of Gauge Theories with BRST Symmetry
• SU_L(2) X U_Y(1)-invariant description of the bilepton contribution to the WWV vertex in the minimal 331 model
• Three loop MSbar renormalization of QCD in the maximal abelian gauge
• Maximal Abelian gauge and a generalized BRST transformation
• U_e(1)--covariant R_ξ--gauge for the two Higgs doublet model
• Renormalization group aspects of the local composite operator method
• MOM renormalization group functions in the maximal abelian gauge
• Maximal abelian and Curci-Ferrari gauges in momentum subtraction at three loops
• Renormalization of QCD in the interpolating momentum subtraction scheme at three loops
• Stability of chromomagnetic condensation and mass generation for confinement in SU(2) Yang-Mills theory
• Composite operator and condensate in the $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group
• Dimensional transmutation in the longitudinal sector of equivariantly gauge-fixed Yang-Mills theory
• Ultraviolet Behavior of the Gluon Propagator in the Maximal Abelian Gauge
• A modification of Faddeev-Popov approach free from Gribov ambiguity