Wave Propagation in Gravitational Systems: Late Time Behavior

It is well-known that the dominant late time behavior of waves propagating on a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have also been studied. This paper presents a systematic treatment of the tail phenomenon for a broad class of models via a Green's function formalism and establishes the following. (i) The tail is governed by a cut of the frequency Green's function $\tilde G(\omega)$ along the $-$~Im~$\omega$ axis, generalizing the Schwarzschild result. (ii) The $\omega$ dependence of the cut is determined by the asymptotic but not the local structure of space. In particular it is independent of the presence of a horizon, and has the same form for the case of a star as well. (iii) Depending on the spatial asymptotics, the late time decay is not necessarily a power law in time. The Schwarzschild case with a power-law tail is exceptional among the class of the potentials having a logarithmic spatial dependence. (iv) Both the amplitude and the time dependence of the tail for a broad class of models are obtained analytically. (v) The analytical results are in perfect agreement with numerical calculations

Generalized Classical BRST Cohomology and Reduction of Poisson Manifolds

In this paper, we formulate a generalization of the classical BRST construction which applies to the case of the reduction of a poisson manifold by a submanifold. In the case of symplectic reduction, our procedure generalizes the usual classical BRST construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold, \ie\ the case of reducible ``first class'' constraints. In particular, our procedure yields a method to deal with ``second-class'' constraints. We construct the BRST complex and compute its cohomology. BRST cohomology vanishes for negative dimension and is isomorphic as a poisson algebra to the algebra of smooth functions on the reduced poisson manifold in zero dimension. We then show that in the general case of reduction of poisson manifolds, BRST cohomology cannot be identified with the cohomology of vertical differential forms.Comment: 3

Mapping Class Group Actions on Quantum Doubles

We study representations of the mapping class group of the punctured torus on the double of a finite dimensional possibly non-semisimple Hopf algebra that arise in the construction of universal, extended topological field theories. We discuss how for doubles the degeneracy problem of TQFT's is circumvented. We find compact formulae for the ${\cal S}^{\pm 1}$-matrices using the canonical, non degenerate forms of Hopf algebras and the bicrossed structure of doubles rather than monodromy matrices. A rigorous proof of the modular relations and the computation of the projective phases is supplied using Radford's relations between the canonical forms and the moduli of integrals. We analyze the projective $SL(2, Z)$-action on the center of $U_q(sl_2)$ for $q$ an $l=2m+1$-st root of unity. It appears that the $3m+1$-dimensional representation decomposes into an $m+1$-dimensional finite representation and a $2m$-dimensional, irreducible representation. The latter is the tensor product of the two dimensional, standard representation of $SL(2, Z)$ and the finite, $m$-dimensional representation, obtained from the truncated TQFT of the semisimplified representation category of $U_q(sl_2)\,$.Comment: 45 page

Localized Endomorphisms of the Chiral Ising Model

Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms $\varrho_1^{\rm loc}$ and $\varrho_{1/2}^{\rm loc}$. It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence $\pi_0\circ\varrho_1^{\rm loc}\cong\pi_1$ and $\pi_0\circ\varrho_{1/2}^{\rm loc}\cong\pi_{1/2}$ holds. Araki's formalism of the selfdual CAR algebra is used for the proof. We prove local normality and extend representations and localized endomorphisms to a global algebra of observables which is generated by local von Neumann algebras on the punctured circle. In this framework, we manifestly prove fusion rules and derive statistics operators.Comment: 41 pages, latex2

Extracting Br(omega->pi^+ pi^-) from the Time-like Pion Form-factor

We extract the G-parity-violating branching ratio Br(omega->pi^+ pi^-) from the effective rho-omega mixing matrix element Pi_{rho omega}(s), determined from e^+e^- -> pi^+ pi^- data. The omega->pi^+ pi^- partial width can be determined either from the time-like pion form factor or through the constraint that the mixed physical propagator D_{rho omega}^{mu nu}(s) possesses no poles. The two procedures are inequivalent in practice, and we show why the first is preferred, to find finally Br(omega->pi^+ pi^-) = 1.9 +/- 0.3%.Comment: 12 pages (published version

A Compact Beam Stop for a Rare Kaon Decay Experiment

We describe the development and testing of a novel beam stop for use in a rare kaon decay experiment at the Brookhaven AGS. The beam stop is located inside a dipole spectrometer magnet in close proximity to straw drift chambers and intercepts a high-intensity neutral hadron beam. The design process, involving both Monte Carlo simulations and beam tests of alternative beam-stop shielding arrangements, had the goal of minimizing the leakage of particles from the beam stop and the resulting hit rates in detectors, while preserving maximum acceptance for events of interest. The beam tests consisted of measurements of rates in drift chambers, scintilation counter hodoscopes, a gas threshold Cherenkov counter, and a lead glass array. Measurements were also made with a set of specialized detectors which were sensitive to low-energy neutrons, photons, and charged particles. Comparisons are made between these measurements and a detailed Monte Carlo simulation.Comment: 39 pages, 14 figures, submitted to Nuclear Instruments and Method

Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the external curvature of the constraint manifold, the (Riemannian) curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is an example of geometric phase, closely related to that originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the external curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.Comment: 27 pages with 1 figure, submitted to Phys. Rev.

On the spherical-axial transition in supernova remnants

A new law of motion for supernova remnant (SNR) which introduces the quantity of swept matter in the thin layer approximation is introduced. This new law of motion is tested on 10 years observations of SN1993J. The introduction of an exponential gradient in the surrounding medium allows to model an aspherical expansion. A weakly asymmetric SNR, SN1006, and a strongly asymmetric SNR, SN1987a, are modeled. In the case of SN1987a the three observed rings are simulated.Comment: 19 figures and 14 pages Accepted for publication in Astrophysics & Space Science in the year 201