363 research outputs found
The genus and the category of configuration spaces
In this paper configuration spaces of smooth manifolds are considered. The
accent is made on actions of certain groups (mostly -tori) on this spaces by
permuting their points. For such spaces the cohomological index, the genus in
the sense of Krasnosel'skii-Schwarz, and the equivariant
Lyusternik-Schnirelmann category are estimated from below, and some corollaries
for functions on configuration spaces are deduced
Symplectic areas, quantization, and dynamics in electromagnetic fields
A gauge invariant quantization in a closed integral form is developed over a
linear phase space endowed with an inhomogeneous Faraday electromagnetic
tensor. An analog of the Groenewold product formula (corresponding to Weyl
ordering) is obtained via a membrane magnetic area, and extended to the product
of N symbols. The problem of ordering in quantization is related to different
configurations of membranes: a choice of configuration determines a phase
factor that fixes the ordering and controls a symplectic groupoid structure on
the secondary phase space. A gauge invariant solution of the quantum evolution
problem for a charged particle in an electromagnetic field is represented in an
exact continual form and in the semiclassical approximation via the area of
dynamical membranes.Comment: 39 pages, 17 figure
Analogues of the central point theorem for families with -intersection property in
In this paper we consider families of compact convex sets in
such that any subfamily of size at most has a nonempty intersection. We
prove some analogues of the central point theorem and Tverberg's theorem for
such families
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