Fourier Transforms of Lorentz Invariant Functions

Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail, and the results for 1+n dimensions are given.Comment: 15 pages, 1 figur

Coherent states for a quantum particle on a circle

The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra $[\hat J,U]=U$, where $U$ is unitary, which is a direct consequence of the Heisenberg algebra $[\hat \phi, \hat J]=i$, but it is more adequate for the study of the circlular motion.Comment: 23 pages LaTeX, uses ioplppt.st

van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes

The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3) One loop approximations to functional integrals. (4) The theory of caustics in geometrical optics and ultrasonics. (5) The focussing and defocussing of geodesic flows in Riemannian manifolds. While all of these topics are interrelated, the present paper is particularly concerned with the last case and presents extensive theoretical developments that aid in the computation of the van Vleck determinant associated with geodesic flows in Lorentzian spacetimes. {\sl A fortiori} these developments have important implications for the entire array of topics indicated. PACS: 04.20.-q, 04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.Comment: plain LaTeX, 18 page

The next challenge for world wide robotized tele-echography experiment (WORTEX 2012): from engineering success to healthcare delivery.

Access to good quality healthcare remains difficult for many patients whether they live in developed or developing countries. In developed countries, specialist medical expertise is concentrated in major hospitals in urban settings both to improve clinical outcomes and as a strategy to reduce the costs of specialist healthcare delivery. In developing countries, millions of people have limited, if any, routine access to a healthcare system and due to economic and cultural factors the accessibility of any services may be restricted. In both cases, geographical, socio-political, cultural and economic factors produce ‘medically isolated areas’ where patients find themselves disadvantaged in terms of timely diagnosis and expert and/or expensive treatment. The robotized teleechography approach, also referred to as robotized teleultrasound, offers a potential solution to diagnostic imaging in medically isolated areas. It is designed for patients requiring ultrasound scans for routine care (e.g., ante natal care) and for diagnostic imaging to investigate acute and medical emergencies conditions, including trauma care and responses to natural disasters such as earthquakes. The robotized teleechography system can hold any standard ultrasound probe; this lightweight system is positioned on the patient’s body by a healthcare assistant. The medical expert, a clinician with expertise in ultrasound imaging and diagnosis, is in a distant location and, using a dedicated joystick, remotely controls the scanning via any available communication link (Internet, satellite). The WORTEX2012 intercontinental trials of the system conducted last year successfully demonstrated the feasibility of remote robotized tele-echography in a range of cultural, technical and clinical contexts. In addition to the engineering success, these trials provided positive feedback from the participating clinicians and patients on using the system and on the system’s perceived potential to transform healthcare in medically isolated areas. The next challenge is to show evidence that this innovative technology can deliver on its promise if introduced into routine healthcare

Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory

We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system during a given time interval. In particular we investigate the case that this subspace is a region of the configuration space. This corresponds to a particular class of coarse grainings of spacetime regions. We consider the arrival time problem and the problem of time in reparametrization invariant theories as for example in canonical quantum gravity. Decoherence conditions and probabilities for those application are derived. The resulting decoherence condition does not depend on the explicit form of the restricted propagator that was problematic for generalizations such as application in quantum cosmology. Closely related is the problem of tunnelling time as well as the quantum Zeno effect. Some interpretational comments conclude, and we discuss the applicability of this formalism to deal with the arrival time problem.Comment: 23 pages, Few changes and added references in v

van Vleck determinants: traversable wormhole spacetimes

Calculating the van Vleck determinant in traversable wormhole spacetimes is an important ingredient in understanding the physical basis behind Hawking's chronology protection conjecture. This paper presents extensive computations of this object --- at least in the short--throat flat--space approximation. An important technical trick is to use an extension of the usual junction condition formalism to probe the full Riemann tensor associated with a thin shell of matter. Implications with regard to Hawking's chronology protection conjecture are discussed. Indeed, any attempt to transform a single isolated wormhole into a time machine results in large vacuum polarization effects sufficient to disrupt the internal structure of the wormhole before the onset of Planck scale physics, and before the onset of time travel. On the other hand, it is possible to set up a putative time machine built out of two or more wormholes, each of which taken in isolation is not itself a time machine. Such ``Roman configurations'' are much more subtle to analyse. For some particularly bizarre configurations (not traversable by humans) the vacuum polarization effects can be arranged to be arbitrarily small at the onset of Planck scale physics. This indicates that the disruption scale has been pushed down into the Planck slop. Ultimately, for these configurations, questions regarding the truth or falsity of Hawking's chronology protection can only be addressed by entering the uncharted wastelands of full fledged quantum gravity.Comment: 42 pages, ReV_TeX 3.

Path Integrals and Their Application to Dissipative Quantum Systems

Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time Path Integral Dissipative Systems - Introduction - Environment as Collection of Harmonic Oscillators - Effective Action Damped Harmonic Oscillator - Partition Function - Ground State Energy and Density of States - Position Autocorrelation FunctionComment: 55 pages, 13 figures. To be published in "Coherent Evolution in Noisy Environments", Lecture Notes in Physics (http://link.springer.de/series/lnpp/) (Springer Verlag, Berlin-Heidelberg-New York

Path Integrals on a Compact Manifold with Non-negative Curvature

A typical path integral on a manifold, $M$ is an informal expression of the form \frac{1}{Z}\int_{\sigma \in H(M)} f(\sigma) e^{-E(\sigma)}\mathcal{D}\sigma, \nonumber where $H(M)$ is a Hilbert manifold of paths with energy $E(\sigma) < \infty$, $f$ is a real valued function on $H(M)$, $\mathcal{D}\sigma$ is a \textquotedblleft Lebesgue measure \textquotedblright and $Z$ is a normalization constant. For a compact Riemannian manifold $M$, we wish to interpret $\mathcal{D}\sigma$ as a Riemannian \textquotedblleft volume form \textquotedblright over $H(M)$, equipped with its natural $G^{1}$ metric. Given an equally spaced partition, ${\mathcal{P}}$ of $[0,1],$ let H_{{\mathcal{P}}%}(M) be the finite dimensional Riemannian submanifold of $H(M)$ consisting of piecewise geodesic paths adapted to $\mathcal{P.}$ Under certain curvature restrictions on $M,$ it is shown that $$\frac{1}{Z_{{\mathcal{P}}}}e^{-{1/2}E(\sigma)}dVol_{H_{{\mathcal{P}}}}(\sigma)\to\rho(\sigma)d\nu(\sigma)\text{as}\mathrm{mesh}({\mathcal{P}})\to0,$$ where $Z_{{\mathcal{P}}}$ is a \textquotedblleft normalization\textquotedblright constant, $E:H(M) \to\lbrack0,\infty)$ is the energy functional, Vol_{H_{{\mathcal{P}}%}} is the Riemannian volume measure on $H_{\mathcal{P}}(M) ,$ $\nu$ is Wiener measure on continuous paths in $M,$ and $\rho$ is a certain density determined by the curvature tensor of $M.

Phase Space Reduction and Vortex Statistics: An Anyon Quantization Ambiguity

We examine the quantization of the motion of two charged vortices in a Ginzburg--Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be implemented either in the reduced phase space or Dirac-Gupta-Bleuler formalism. Using the intrinsic formulation of statistics, we show that these two ways of implementing the constraints are inequivalent unless the vortices are quantized with conventional statistics; either fermionic or bosonic.Comment: 14 pages, PHYZZ

Radiative multipole moments of integer-spin fields in curved spacetime

Radiative multipole moments of scalar, electromagnetic, and linearized gravitational fields in Schwarzschild spacetime are computed to third order in v in a weak-field, slow-motion approximation, where v is a characteristic velocity associated with the motion of the source. To zeroth order in v, a radiative moment of order l is given by the corresponding source moment differentiated l times with respect to retarded time. At second order in v, additional terms appear inside the spatial integrals. These are near-zone corrections which depend on the detailed behavior of the source. At third order in v, the correction terms occur outside the spatial integrals, so that they do not depend on the detailed behavior of the source. These are wave-propagation corrections which are heuristically understood as arising from the scattering of the radiation by the spacetime curvature surrounding the source. Our calculations show that the wave-propagation corrections take a universal form which is independent of multipole order and field type. We also show that in general relativity, temporal and spatial curvatures contribute equally to the wave-propagation corrections.Comment: 34 pages, ReVTe