Yang-Mills Fields and Riemannian Geometry

Abstract

It is possible to define new, gauge invariant variables in the Hilbert space of Yang-Mills theories which manifestly implement Gauss' law on physical states. These variables have furthermore a geometrical meaning, and allow one to uncover further constraints physical states must satisfy. For gauge group $SU(2)$, the underlying geometry is Riemannian and based on the group $GL(3)$. The formalism allows also for the inclusion of static color sources and the extension to gauge groups $SU(N>2)$, both of which are discussed here.

22 PP., HARVMAC. MINOR TYPOS CORRECTED - FINAL VERSION, TO BE PUBLISHED IN NUCL. PHYS. B

References in corpus (2)

• Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories
• The Wu-Yang Ambiguity Revisited

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