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Register a new userDiffeomorphism invariant measure for finite dimensional geometries
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We consider families of geometries of D--dimensional space, described by a finite number of parameters. Starting from the De Witt metric we extract a unique integration measure which turns out to be a geometric invariant, i.e. independent of the gauge fixed metric used for describing the geometries. The measure is also invariant in form under an arbitrary change of parameters describing the geometries. We prove the existence of geometries for which there are no related gauge fixing surfaces orthogonal to the gauge fibers. The additional functional integration on the conformal factor makes the measure independent of the free parameter intervening in the De Witt metric. The determinants appearing in the measure are mathematically well defined even though technically difficult to compute.
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We describe a class of diffeomorphism invariant SU(N) gauge theories in N^2 dimensions, together with some matter couplings. These theories have (N^2-3)(N^2-1) local degrees of freedom, and have the unusual feature that the constraint associated with time reparametrizations is identically satisfied. A related class of SU(N) theories in N^2-1 dimensions has the constraint algebra of general relativity, but has more degrees of freedom. Non-perturbative quantization of the first type of theory via SU(N) spin networks is briefly outlined.
In a diffeomorphism invariant theory, symmetry breaking may be a mask for coordinate choice.
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