2,794 research outputs found
On spectral types of semialgebraic sets
In this work we prove that a semialgebraic set is
determined (up to a semialgebraic homeomorphism) by its ring
of (continuous) semialgebraic functions while its ring of
(continuous) bounded semialgebraic functions only determines besides a
distinguished finite subset . In addition it holds that the
rings and are isomorphic if and only if
is compact. On the other hand, their respective maximal spectra
and endowed with the Zariski topology are always homeomorphic and
topologically classify a `large piece' of . The proof of this fact requires
a careful analysis of the points of the remainder associated with formal paths.Comment: 22 page
Non-Abelian Monopoles as the Origin of Dark Matter
We suggest that dark matter may be partially constituted by a dilute 't
Hooft-Polyakov monopoles gas. We reach this conclusion by using the
Georgi-Glashow model coupled to a dual kinetic mixing term where is the electromagnetic field and the 't Hooft tensor.
We show that these monopoles carry both (Maxwell) electric and (Georgi-Glashow)
magnetic charges and the electric charge quantization condition is modified in
terms of a dimensionless real parameter. This parameter could be determined
from milli-charged particle experiments.Comment: 5 pp, no figure
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