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 $c\rightarrow \infty .$ 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