A New Gauge Without any Ghost for Yang-Mills Theory

  • A. Burnel
Part of the NATO ASI Series book series (NSSB, volume 144)


Singer’s theorem1 tells us that a global gauge defined as a global section is impossible to find for Yang-Mills theory. This means that any known gauge necessarily involves unphysical fields which are either Faddeev-Popov2 ghost fields or the longitudinal fields in the temporal gauge or both and, in addition, a scalar field in relativistic gauges. The popular axial gauge, which could circumvent Singer’s theorem, is known to be ill-defined3,4. The non-existence of a gauge with only physical degrees of freedom would be a serious difficulty for the physical interpretation of the theory. Fortunately, for Yang-Mills theory, it is possible to find a gauge where only physical degrees of freedom play a dynamical role. It is obvious through the consideration of the simplest possible gauge theory given by the Lagrangian
$$ L = \frac{1}{2}{\dot{x}^2} + \frac{1}{2}{(\dot{y} - z)^2}. $$
. It describes in a gauge invariant way the free motion of a particle on a straight line embedded in a plane. y = 0 corresponds to the usual gauge fixing.


Gauge Theory Scalar Field Global Section Physical Degree Longitudinal Field 
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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • A. Burnel
    • 1
  1. 1.Institut de PhysiqueUniversité de LiègeLiege 1Belgium

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