3,155 research outputs found
Finite Approximations to Quantum Physics: Quantum Points and their Bundles
There exists a physically well motivated method for approximating manifolds
by certain topological spaces with a finite or a countable set of points. These
spaces, which are partially ordered sets (posets) have the power to effectively
reproduce important topological features of continuum physics like winding
numbers and fractional statistics, and that too often with just a few points.
In this work, we develop the essential tools for doing quantum physics on
posets. The poset approach to covering space quantization, soliton physics,
gauge theories and the Dirac equation are discussed with emphasis on physically
important topological aspects. These ideas are illustrated by simple examples
like the covering space quantization of a particle on a circle, and the
sine-Gordon solitons.Comment: 24 pages, 8 figures on a uuencoded postscript file, DSF-T-29/93,
INFN-NA-IV-29/93 and SU-4240-55
On the Duality of Semiantichains and Unichain Coverings
We study a min-max relation conjectured by Saks and West: For any two posets
and the size of a maximum semiantichain and the size of a minimum
unichain covering in the product are equal. For positive we state
conditions on and that imply the min-max relation. Based on these
conditions we identify some new families of posets where the conjecture holds
and get easy proofs for several instances where the conjecture had been
verified before. However, we also have examples showing that in general the
min-max relation is false, i.e., we disprove the Saks-West conjecture.Comment: 10 pages, 3 figure
Neighborhood complexes and Kronecker double coverings
The neighborhood complex is a simplicial complex assigned to a graph
whose connectivity gives a lower bound for the chromatic number of . We
show that if the Kronecker double coverings of graphs are isomorphic, then
their neighborhood complexes are isomorphic. As an application, for integers
and greater than 2, we construct connected graphs and such that
but and . We also construct a
graph such that and the Kneser graph are not
isomorphic but their Kronecker double coverings are isomorphic.Comment: 10 pages. Some results concerning box complexes are deleted. to
appear in Osaka J. Mat
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