1,477 research outputs found
(In)finite extensions of algebras from their Inonu-Wigner contractions
The way to obtain massive non-relativistic states from the Poincare algebra
is twofold. First, following Inonu and Wigner the Poincare algebra has to be
contracted to the Galilean one. Second, the Galilean algebra is to be extended
to include the central mass operator. We show that the central extension might
be properly encoded in the non-relativistic contraction. In fact, any
Inonu-Wigner contraction of one algebra to another, corresponds to an infinite
tower of abelian extensions of the latter. The proposed method is
straightforward and holds for both central and non-central extensions. Apart
from the Bargmann (non-zero mass) extension of the Galilean algebra, our list
of examples includes the Weyl algebra obtained from an extension of the
contracted SO(3) algebra, the Carrollian (ultra-relativistic) contraction of
the Poincare algebra, the exotic Newton-Hooke algebra and some others. The
paper is dedicated to the memory of Laurent Houart (1967-2011).Comment: 7 pages, revtex style; v2: Minor corrections, references added; v3:
Typos correcte
Scalar Kaluza-Klein modes in a multiply warped braneworld
The Kaluza-Klein (KK) modes of a massive scalar field on a 3-brane embedded
in six dimensional multiply warped spacetime are determined. Due to the
presence of warping along both the extra dimensions the KK mass spectrum splits
into two closely spaced branches which is a distinct feature of this model
compared to the five dimensional Randall-Sundrum model. This new cluster of the
KK mode spectrum is expected to have interesting phenomenological implications
for the upcoming collider experiments. Such a scenario may also be extended for
even larger number of orbifolded extra dimensions.Comment: 10 pages, Revte
The (p,q) String Tension in a Warped Deformed Conifold
We find the tension spectrum of the bound states of p fundamental strings and
q D-strings at the bottom of a warped deformed conifold. We show that it can be
obtained from a D3-brane wrapping a 2-cycle that is stabilized by both electric
and magnetic fluxes. Because the F-strings are Z_M-charged with non-zero
binding energy, binding can take place even if (p,q) are not coprime.
Implications for cosmic strings are briefly discussed.Comment: 17 pages, 1 figur
Quantum mechanical description of Stern-Gerlach experiments
The motion of neutral particles with magnetic moments in an inhomogeneous
magnetic field is described in a quantum mechanical framework. The validity of
the semi-classical approximations which are generally used to describe these
phenomena is discussed. Approximate expressions for the evolution operator are
derived and compared to the exact calculations. Focusing and spin-flip
phenomena are predicted. The reliability of Stern-Gerlach experiments to
measure spin projections is assessed in this framework.Comment: 12 pages, 7 eps figures included, revtex, submitted to PR
Spinor vortices in non-relativistic Chern-Simons theory
The non-relativistic `Dirac' equation of L\'evy-Leblond is used to describe a
spin {\small 1/2} particle interacting with a Chern-Simons gauge field. Static,
purely magnetic, self-dual spinor vortices are constructed. The solution can be
`exported' to a uniform magnetic background field.Comment: 7 pages, Plain Te
No-Go Theorem for Horizon-Shielded Self-Tuning Singularities
We derive a simple no-go theorem relating to self-tuning solutions to the
cosmological constant for observers on a brane, which rely on a singularity in
an extra dimension. The theorem shows that it is impossible to shield the
singularity from the brane by a horizon, unless the positive energy condition
(rho+p >= 0) is violated in the bulk or on the brane. The result holds
regardless of the kinds of fields which are introduced in the bulk or on the
brane, whether Z_2 symmetry is imposed at the brane, or whether higher
derivative terms of the Gauss-Bonnet form are added to the gravitational part
of the action. However, the no-go theorem can be evaded if the three-brane has
spatial curvature. We discuss explicit realizations of such solutions which
have both self-tuning and a horizon shielding the singularity.Comment: 7 pages, 4 figures, revtex; added reference and minor correction
The hierarchy problem, radion mass, localization of gravity and 4D effective Newtonian potential in string theory on
We present a systematical study of brane worlds in string theory on
. Starting with the toroidal compactification of the NS/NS sector
in (D+d) dimensions, we first obtain an effective -dimensional action, and
then compactify one of the spatial dimensions by introducing two
orbifold branes as its boundaries. By combining the Gauss-Codacci and Lanczos
equations, we write down explicitly the general gravitational field equations
on each of the two branes, while using distribution theory we express the
matter field equations on the branes in terms of the discontinuities of the
first derivatives of the matter fields. Afterwards, we address three important
issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the
localization of gravity, the 4-dimensional Newtonian effective potential and
the Yukawa corrections due to the gravitational high-order Kaluza-Klein (KK)
modes. With a very conservative estimation, we find that the radion mass is of
the order of . The gravity is localized on the visible brane, and
the spectrum of the gravitational KK modes is discrete and can be of the order
of TeV. The corrections to the 4-dimensional Newtonian potential from the
higher order of gravitational KK modes are exponentially suppressed and can be
safely neglected in current experiments. In an appendix, we also present a
systematical and pedagogical study of the Gauss-Codacci equations and Israel's
junction conditions across a (D-1)-dimensional hypersurface, which can be
either spacelike or timelike.Comment: Considerably extended, Revtex4, 19 pages, 5 figures, published in
IJMPA, 25, 1661-1698 (2010
Dynamical Stability of Six-Dimensional Warped Brane-Worlds
We study a generalization of the Randall-Sundrum mechanism for generating the
weak/Planck hierarchy, which uses two rather than one warped extra dimension,
and which requires no negative tension branes. A 4-brane with one exponentially
large compact dimension plays the role of the Planck brane. We investigate the
dynamical stability with respect to graviton, graviphoton and radion modes. The
radion is shown to have a tachyonic instability for certain models of the
4-brane stress-energy, while it is stable in others, and massless in a special
case. If stable, its mass is in the milli-eV range, for parameters of the model
which solve the hierarchy problem. The radion is shown to couple to matter with
gravitational strength, so that it is potentially detectable by
submillimeter-range gravity experiments. The radion mass can be increased using
a bulk scalar field in the manner of Goldberger and Wise, but only to order
MeV, due to the effect of the large extra dimension. The model predicts a
natural scale of 10^{13} GeV on the 4-brane, making it a natural setting for
inflation from the ultraviolet brane.Comment: 28 pages, 7 figure
Can degenerate bound states occur in one dimensional quantum mechanics?
We point out that bound states, degenerate in energy but differing in parity,
may form in one dimensional quantum systems even if the potential is
non-singular in any finite domain. Such potentials are necessarily unbounded
from below at infinity and occur in several different contexts, such as in the
study of localised states in brane-world scenarios. We describe how to
construct large classes of such potentials and give explicit analytic
expressions for the degenerate bound states. Some of these bound states occur
above the potential maximum while some are below. Various unusual features of
the bound states are described and after highlighting those that are ansatz
independent, we suggest that it might be possible to observe such parity-paired
degenerate bound states in specific mesoscopic systems.Comment: 10 pages, 2 figures, to appear in Europhysics Letter
Covariance systems
We introduce new definitions of states and of representations of covariance
systems. The GNS-construction is generalized to this context. It associates a
representation with each state of the covariance system. Next, states are
extended to states of an appropriate covariance algebra. Two applications are
given. We describe a nonrelativistic quantum particle, and we give a simple
description of the quantum spacetime model introduced by Doplicher et al.Comment: latex with ams-latex, 23 page
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