6,481 research outputs found
A generalization of Voronoi's reduction theory and its application
We consider Voronoi's reduction theory of positive definite quadratic forms
which is based on Delone subdivision. We extend it to forms and Delone
subdivisions having a prescribed symmetry group. Even more general, the theory
is developed for forms which are restricted to a linear subspace in the space
of quadratic forms. We apply the new theory to complete the classification of
totally real thin algebraic number fields which was recently initiated by
Bayer-Fluckiger and Nebe. Moreover, we apply it to construct new best known
sphere coverings in dimensions 9,..., 15.Comment: 31 pages, 2 figures, 2 tables, (v4) minor changes, to appear in Duke
Math.
Generalized Sums over Histories for Quantum Gravity I. Smooth Conifolds
This paper proposes to generalize the histories included in Euclidean
functional integrals from manifolds to a more general set of compact
topological spaces. This new set of spaces, called conifolds, includes
nonmanifold stationary points that arise naturally in a semiclasssical
evaluation of such integrals; additionally, it can be proven that sequences of
approximately Einstein manifolds and sequences of approximately Einstein
conifolds both converge to Einstein conifolds. Consequently, generalized
Euclidean functional integrals based on these conifold histories yield
semiclassical amplitudes for sequences of both manifold and conifold histories
that approach a stationary point of the Einstein action. Therefore sums over
conifold histories provide a useful and self-consistent starting point for
further study of topological effects in quantum gravity. Postscript figures
available via anonymous ftp at black-hole.physics.ubc.ca (137.82.43.40) in file
gen1.ps.Comment: 81pp., plain TeX, To appear in Nucl. Phys.
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