Fundamental Aspects of Quantum Theory pp 423-424 | Cite as

# A New Gauge Without any Ghost for Yang-Mills Theory

Chapter

## Abstract

Singer’s theorem. 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.

^{1}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-Popov^{2}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-defined^{3,4}. 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$$ L = \frac{1}{2}{\dot{x}^2} + \frac{1}{2}{(\dot{y} - z)^2}. $$

## Keywords

Gauge Theory Scalar Field Global Section Physical Degree Longitudinal Field
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## References

- 1.I.M. Singer, Some Remarks on the Gribov Ambiguity, Comm.Math.Phys.60; 7 (1978).MathSciNetADSMATHCrossRefGoogle Scholar
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- 3.N. Nakanishi, Singularity-Free Canonical Theory of Gauge Fields in the Axial Gauge, Progr.Theor.Phys.67;965 (1982).MathSciNetADSMATHCrossRefGoogle Scholar
- 4.A. Burnel and M. Van der Rest-Jaspers, Consistent Formulation of the Space-Like Axial Gauge, Phys.Rev.D28:3121 (1983).ADSGoogle Scholar
- 5.L.D. Faddeev and A.A. Slavnov, "Gauge Fields. Introduction to Quantum Theory", Benjamin, Reading,Mass. (1980).MATHGoogle Scholar
- 6.A. Burnel, Natural Gauge without any Ghost for Yang-Mills Theory, Phys. Rev.D32:450 (1985).MathSciNetADSGoogle Scholar

## Copyright information

© Plenum Press, New York 1986