It is proposed that the gravitational field can be described in an invariant way by its “holonomy set” involving paths in Minkowski space and points in the Lorentz group. The differentiable manifold of gravity does not enter as a basic object but is constructed in a manner depending on the field configuration. Thus there is no diffeomorphism symmetry in this description of gravity, nor is the topology of space-time fixed at the outset. It is therefore proposed that the “holonomy description” of gravity provides a much better starting point for the analysis of quantum gravity. Striking similarities with Yang-Mills gauge theories emerge which shed light on the problem of whether gravity is or is not a gauge theory.
KeywordsManifold Gauge Theory Quantum Gravity Differential Geometry Gravitational Field
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