4,329 research outputs found
DYNAMICAL GENERALIZATIONS OF THE LAGRANGE SPECTRUM
International audienceWe compute two invariants of topological conjugacy, the upper and lower limits of the inverse of Boshernitzan's ne n , where e n is the smallest measure of a cylinder of length n, for three families of symbolic systems, the natural codings of rotations and three-interval exchanges and the Arnoux-Rauzy systems. The sets of values of these invariants for a given family of systems generalize the Lagrange spectrum, which is what we get for the family of rotations with the upper limit of 1 nen. The Lagrange spectrum is the set of finite values of L(α) for all irrational numbers α, where L(α) is the largest constant c such that |α â p q | †1 cq 2 for infinitely many integers p and q (a variant is known as the Markov spectrum, see Section 1.3 below). It was recently remarked that this arithmetic definition can be replaced by a dynamical definition involving the irrational rotations of angle α, through their natural coding by the partition {[0, 1 â α[, [1 â α, 1[}. Namely, as we prove in Theorem 2.4 below which was never written before, L(α) is also the upper limit of the inverse of the so-called Boshernitzan's ne n , where e n is the smallest (Lebesgue) measure of the nonempty cylinders of length n. Thus, for any symbolic dynamical system, it is interesting to compute two new invariants of topological conjugacy, lim sup nâ+â 1 ne
Bi-gravity with a single graviton
We analyze a bi-gravity model based on the first order formalism, having as
fundamental variables two tetrads but only one Lorentz connection. We show that
on a large class of backgrounds its linearization agrees with general
relativity. At the non-linear level, additional degrees of freedom appear, and
we reveal the mechanism hiding them around the special backgrounds. We further
argue that they do not contain a massive graviton, nor the Boulware-Deser
ghost. The model thus propagates only one graviton, whereas the nature of the
additional degrees of freedom remains to be investigated. We also present a
foliation-preserving deformation of the model, which keeps all symmetries
except time diffeomorphisms and has three degrees of freedom.Comment: 29 page
Dynamical Supersymmetry Breaking
Supersymmetry is one of the most plausible and theoretically motivated
frameworks for extending the Standard Model. However, any supersymmetry in
Nature must be a broken symmetry. Dynamical supersymmetry breaking (DSB) is an
attractive idea for incorporating supersymmetry into a successful description
of Nature. The study of DSB has recently enjoyed dramatic progress, fueled by
advances in our understanding of the dynamics of supersymmetric field theories.
These advances have allowed for direct analysis of DSB in strongly coupled
theories, and for the discovery of new DSB theories, some of which contradict
early criteria for DSB. We review these criteria, emphasizing recently
discovered exceptions. We also describe, through many examples, various
techniques for directly establishing DSB by studying the infrared theory,
including both older techniques in regions of weak coupling, and new techniques
in regions of strong coupling. Finally, we present a list of representative DSB
models, their main properties, and the relations between them.Comment: 113 pages, Revtex. Minor changes, references added and corrected. To
appear in Reviews of Modern Physic
The rigid body dynamics: classical and algebro-geometric integration
The basic notion for a motion of a heavy rigid body fixed at a point in
three-dimensional space as well as its higher-dimensional generalizations are
presented. On a basis of Lax representation, the algebro-geometric integration
procedure for one of the classical cases of motion of three-dimensional rigid
body - the Hess-Appel'rot system is given. The classical integration in Hess
coordinates is presented also. For higher-dimensional generalizations, the
special attention is paid in dimension four. The L-A pairs and the classical
integration procedures for completely integrable four-dimensional rigid body so
called the Lagrange bitop as well as for four-dimensional generalization of
Hess-Appel'rot system are given. An -dimensional generalization of the
Hess-Appel'rot system is also presented and its Lax representation is given.
Starting from another Lax representation for the Hess-Appel'rot system, a
family of dynamical systems on is constructed. For five cases from the
family, the classical and algebro-geometric integration procedures are
presented. The four-dimensional generalizations for the Kirchhoff and the
Chaplygin cases of motion of rigid body in ideal fluid are defined. The results
presented in the paper are part of results obtained in last decade.Comment: Zb. Rad.(Beogr.), 16(24), 2013 (accepted for publication); 43 page
Dynamical solution to the problem at TeV scale
We introduce a new confining force (\mu-color) at TeV scale to dynamically
generate a supersymmetry preserving mass scale which would replace the \mu
parameter in the minimal supersymmetric standard model (MSSM). We discuss the
Higgs phenomenology and also the pattern of soft supersymmetry breaking
parameters allowing the correct electroweak symmetry breaking within the
\mu-color model, which have quite distinctive features from the MSSM and also
from other generalizations of the MSSM.Comment: 12 pages, REVte
The Lagrange spectrum of a Veech surface has a Hall ray
We study Lagrange spectra of Veech translation surfaces, which are a
generalization of the classical Lagrange spectrum. We show that any such
Lagrange spectrum contains a Hall ray. As a main tool, we use the boundary
expansion developed by Bowen and Series to code geodesics in the corresponding
Teichm\"uller disk and prove a formula which allows to express large values in
the Lagrange spectrum as sums of Cantor sets.Comment: 30 pages, 5 figures. Minor revisio
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