18,634 research outputs found
Bijective evaluation of the connection coefficients of the double coset algebra
This paper is devoted to the evaluation of the generating series of the
connection coefficients of the double cosets of the hyperoctahedral group.
Hanlon, Stanley, Stembridge (1992) showed that this series, indexed by a
partition , gives the spectral distribution of some random real matrices
that are of interest in random matrix theory. We provide an explicit evaluation
of this series when in terms of monomial symmetric functions. Our
development relies on an interpretation of the connection coefficients in terms
of locally orientable hypermaps and a new bijective construction between
locally orientable partitioned hypermaps and some permuted forests.Comment: 12 pages, 5 figure
Effective 4D propagation of a charged scalar particle in Visser brane world
In this work we extend an analysis due to Visser of the effective propagation
of a neutral scalar particle on a brane world scenario which is a particular
solution of the five dimensional Einstein-Maxwell equations with cosmological
constant having an electric field pointing in the extra spatial dimension. We
determine the dispersion relations of a charged scalar particle to first order
in a perturbative analysis around those of the neutral particle. Since
depending on whether the particle is charged or not the dispersion relations
change, we could collect bulk information, namely the presence of the electric
field, by studying the 4D dynamics of the particles.Comment: 12 pages, 5 figure
The Enigma of the Dark Matter
One of the great scientific enigmas still unsolved, the existence of dark
matter, is reviewed. Simple gravitational arguments imply that most of the mass
in the Universe, at least 90%, is some (unknown) non-luminous matter. Some
particle candidates for dark matter are discussed with particular emphasis on
the neutralino, a particle predicted by the supersymmetric extension of the
Standard Model of particle physics. Experiments searching for these relic
particles, carried out by many groups around the world, are also discussed.
These experiments are becoming more sensitive every year and in fact one of the
collaborations claims that the first direct evidence for dark matter has
already been observed.Comment: Invited review article for the journal Contemporary Physics. The
level is suitable for researchers which are non-specialists in the subject,
and also for students. Latex, 20 pages, 5 figure
Real sector of the nonminimally coupled scalar field to self-dual gravity
A scalar field nonminimally coupled to gravity is studied in the canonical
framework, using self-dual variables. The corresponding constraints are first
class and polynomial. To identify the real sector of the theory, reality
conditions are implemented as second class constraints, leading to three real
configurational degrees of freedom per space point. Nevertheless, this
realization makes non-polynomial some of the constraints. The original complex
symplectic structure reduces to the expected real one, by using the appropriate
Dirac brackets. For the sake of preserving the simplicity of the constraints,
an alternative method preventing the use of Dirac brackets, is discussed. It
consists of converting all second class constraints into first class by adding
extra variables. This strategy is implemented for the pure gravity case.Comment: Latex file, 22 pages, no figure
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