159 research outputs found
AdS-Carroll Branes
Coset methods are used to determine the action of a co-dimension one brane
(domain wall) embedded in (d+1)-dimensional AdS space in the Carroll limit in
which the speed of light goes to zero. The action is invariant under the
non-linearly realized symmetries of the AdS-Carroll spacetime. The
Nambu-Goldstone field exhibits a static spatial distribution for the brane with
a time varying momentum density related to the brane's spatial shape as well as
the AdS-C geometry. The AdS-C vector field dual theory is obtained.Comment: 47 page
Lie Bialgebra Structures for Centrally Extended Two- Dimensional Galilei Algebra and their Lie-Poisson Counterparts
All bialgebra structures for centrally extended Galilei algebra are
classified. The corresponding Lie-Poisson structures on centrally extended
Galilei group are found.Comment: Eq. (11) changed, 15 pages, LaTeX fil
Galilean Limit of Equilibrium Relativistic Mass Distribution
The low-temperature form of the equilibrium relativistic mass distribution is
subject to the Galilean limit by taking In this limit
the relativistic Maxwell-Boltzmann distribution passes to the usual
nonrelativistic form and the Dulong-Petit law is recovered.Comment: TAUP-2081-9
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
On the Relationship of Quantum Mechanics to Classical Electromagnetism and Classical Relativistic Mechanics
Some connections between quantum mechanics and classical physics are
explored. The Planck-Einstein and De Broglie relations, the wavefunction and
its probabilistic interpretation, the Canonical Commutation Relations and the
Maxwell--Lorentz Equation may be understood in a simple way by comparing
classical electromagnetism and the photonic description of light provided by
classical relativistic kinematics. The method used may be described as `inverse
correspondence' since quantum phenomena become apparent on considering the low
photon number density limit of classical electromagnetism. Generalisation to
massive particles leads to the Klein--Gordon and Schr\"{o}dinger Equations. The
difference between the quantum wavefunction of the photon and a classical
electromagnetic wave is discussed in some detail.Comment: 14 pages, no figures, no table
Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory
Newton's standard theory of gravitation is reformulated as a {\it gauge}
theory of the {\it extended} Galilei Group. The Action principle is obtained by
matching the {\it gauge} technique and a suitable limiting procedure from the
ADM-De Witt action of general relativity coupled to a relativistic mass-point.Comment: 51 pages , compress, uuencode LaTex fil
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
Local scale invariance and strongly anisotropic equilibrium critical systems
A new set of infinitesimal transformations generalizing scale invariance for
strongly anisotropic critical systems is considered. It is shown that such a
generalization is possible if the anisotropy exponent \theta =2/N, with N=1,2,3
... Differential equations for the two-point function are derived and
explicitly solved for all values of N. Known special cases are conformal
invariance (N=2) and Schr\"odinger invariance (N=1). For N=4 and N=6, the
results contain as special cases the exactly known scaling forms obtained for
the spin-spin correlation function in the axial next nearest neighbor spherical
(ANNNS) model at its Lifshitz points of first and second order.Comment: 4 pages Revtex, no figures, with file multicol.sty, to appear in PR
Centers of Mass and Rotational Kinematics for the Relativistic N-Body Problem in the Rest-Frame Instant Form
In the Wigner-covariant rest-frame instant form of dynamics it is possible to
develop a relativistic kinematics for the N-body problem. The Wigner
hyperplanes define the intrinsic rest frame and realize the separation of the
center-of-mass. Three notions of {\it external} relativistic center of mass can
be defined only in terms of the {\it external} Poincar\'e group realization.
Inside the Wigner hyperplane, an {\it internal} unfaithful realization of the
Poincar\'e group is defined. The three concepts of {\it internal} center of
mass weakly {\it coincide} and are eliminated by the rest-frame conditions. An
adapted canonical basis of relative variables is found. The invariant mass is
the Hamiltonian for the relative motions. In this framework we can introduce
the same {\it dynamical body frames}, {\it orientation-shape} variables, {\it
spin frame} and {\it canonical spin bases} for the rotational kinematics
developed for the non-relativistic N-body problem.Comment: 78 pages, revtex fil
Schild's Null Strings in Flat and Curved Backgrounds
Schild's null (tensionless) strings are discussed in certain flat and curved
backgrounds. We find closed, stationary, null strings as natural configurations
existing on the horizons of spacetimes which possess such null hypersurfaces.
Examples of these are obtained in Schwarzschild and Rindler spacetimes. A
dynamic null string is also identified in Rindler spacetime. Furthermore, a
general prescription (with explicit examples) is outlined by means of which
null string configurations can be obtained in a large class of cosmological
backgrounds.Comment: RevTex 3.0, 14 Pages, no figure
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