The role of diffeomorphisms in the integration over a finite dimensional space of geometries

Details The role of diffeomorphisms in the integration over a finite dimensional space of geometries The role of diffeomorphisms in the integration over a finite dimensional space of geometries

1997-09-24

arxiv.org/abs/hep-lat/9709101v1

Nucl.Phys.Proc.Suppl. 63 (1998) 760-762

Physics

High Energy Physics

High Energy Physics - Lattice

3 pages, LaTeX, Talk given at LATTICE'97, Edinburgh

Scientific paper

10.1016/S0920-5632(97)00896-7

Starting from the De Witt supermetric and limiting ourselves to a family of geometries characterized by a finite number of geometric invariants we extract the unique integration measure. Such a measure 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. The additional functional integration on the conformal factor makes the measure independent of the free parameter intervening in the De Witt supermetric. The differences between the case D=2 and $D>2$ are evidenced.

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