Quark confinement and long-range gauge fields in quantum chromodynamics

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Abstract
The influence of long-range gauge fields on the quark-antiquark static potential in the SU(2) Yang-Mills theory is discussed. The long-range fields considered are Wu-Yang monopole fields and superpositions of monopoles. The instantaneous Coulomb interaction, which is shown to be responsible for asymptotic freedom, is computed in a background monopole field. The effect of the background field produced by a superposition of monopoles is computed using the dilute-gas approximation. The resulting potential is attractive and infrared divergent. The infrared divergence may be an indication that long-range vacuum fields are the basis of quark confinement. It is argued that formation of a string of color-electric flux between the quarks lowers their energy relative to the instantaneous Coulomb energy.