90 research outputs found
Hamiltonian Gravity and Noncommutative Geometry
A version of foliated spacetime is constructed in which the spatial geometry
is described as a time dependent noncommutative geometry. The ADM version of
the gravitational action is expressed in terms of these variables. It is shown
that the vector constraint is obtained without the need for an extraneous shift
vector in the action.Comment: 22 pages, AMS-LaTeX. Some improvements - mainly to sections 8 and 9.
Typographical errors to equations in appendix correcte
Quantization of Equivariant Vector Bundles
The quantization of vector bundles is defined. Examples are constructed for
the well controlled case of equivariant vector bundles over compact coadjoint
orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple
symmetry group.) In preparation for the main result, the quantization of
coadjoint orbits is discussed in detail.
This subject should not be confused with the quantization of the total space
of a vector bundle such as the cotangent bundle.Comment: 33 pages. AMS-LaTeX. Contains table-of-contents, so run LaTeX 3
times. Minor improvements, 2 added references. Continued by math.QA/980811
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