3,425 research outputs found
Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces
We discuss various infinite-dimensional configuration spaces that carry
measures quasiinvariant under compactly-supported diffeomorphisms of a manifold
M corresponding to a physical space. Such measures allow the construction of
unitary representations of the diffeomorphism group, which are important to
nonrelativistic quantum statistical physics and to the quantum theory of
extended objects in d-dimensional Euclidean space. Special attention is given
to measurable structure and topology underlying measures on generalized
configuration spaces obtained from self-similar random processes (both for d =
1 and d > 1), which describe infinite point configurations having accumulation
points
Some Variations on Maxwell's Equations
In the first sections of this article, we discuss two variations on Maxwell's
equations that have been introduced in earlier work--a class of nonlinear
Maxwell theories with well-defined Galilean limits (and correspondingly
generalized Yang-Mills equations), and a linear modification motivated by the
coupling of the electromagnetic potential with a certain nonlinear Schroedinger
equation. In the final section, revisiting an old idea of Lorentz, we write
Maxwell's equations for a theory in which the electrostatic force of repulsion
between like charges differs fundamentally in magnitude from the electrostatic
force of attraction between unlike charges. We elaborate on Lorentz'
description by means of electric and magnetic field strengths, whose governing
equations separate into two fully relativistic Maxwell systems--one describing
ordinary electromagnetism, and the other describing a universally attractive or
repulsive long-range force. If such a force cannot be ruled out {\it a priori}
by known physical principles, its magnitude should be determined or bounded
experimentally. Were it to exist, interesting possibilities go beyond Lorentz'
early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch
v. 2: discussion revised, factors of 4\pi corrected in some equation
Gesture analysis for physics education researchers
Systematic observations of student gestures can not only fill in gaps in
students' verbal expressions, but can also offer valuable information about
student ideas, including their source, their novelty to the speaker, and their
construction in real time. This paper provides a review of the research in
gesture analysis that is most relevant to physics education researchers and
illustrates gesture analysis for the purpose of better understanding student
thinking about physics.Comment: 14 page
On the virial coefficients of nonabelian anyons
We study a system of nonabelian anyons in the lowest Landau level of a strong
magnetic field. Using diagrammatic techniques, we prove that the virial
coefficients do not depend on the statistics parameter. This is true for all
representations of all nonabelian groups for the statistics of the particles
and relies solely on the fact that the effective statistical interaction is a
traceless operator.Comment: 9 pages, 3 eps figure
Quantum chaos, random matrix theory, and statistical mechanics in two dimensions - a unified approach
We present a theory where the statistical mechanics for dilute ideal gases
can be derived from random matrix approach. We show the connection of this
approach with Srednicki approach which connects Berry conjecture with
statistical mechanics. We further establish a link between Berry conjecture and
random matrix theory, thus providing a unified edifice for quantum chaos,
random matrix theory, and statistical mechanics. In the course of arguing for
these connections, we observe sum rules associated with the outstanding
counting problem in the theory of braid groups. We are able to show that the
presented approach leads to the second law of thermodynamics.Comment: 23 pages, TeX typ
A Topological String: The Rasetti-Regge Lagrangian, Topological Quantum Field Theory, and Vortices in Quantum Fluids
The kinetic part of the Rasetti-Regge action I_{RR} for vortex lines is
studied and links to string theory are made. It is shown that both I_{RR} and
the Polyakov string action I_{Pol} can be constructed with the same field X^mu.
Unlike I_{NG}, however, I_{RR} describes a Schwarz-type topological quantum
field theory. Using generators of classical Lie algebras, I_{RR} is generalized
to higher dimensions. In all dimensions, the momentum 1-form P constructed from
the canonical momentum for the vortex belongs to the first cohomology class
H^1(M,R^m) of the worldsheet M swept-out by the vortex line. The dynamics of
the vortex line thus depend directly on the topology of M. For a vortex ring,
the equations of motion reduce to the Serret-Frenet equations in R^3, and in
higher dimensions they reduce to the Maurer-Cartan equations for so(m).Comment: To appear in Journal of Physics
Cognitive demands of face monitoring: Evidence for visuospatial overload
Young children perform difficult communication tasks better face to face than when they cannot see one another (e.g., Doherty-Sneddon & Kent, 1996). However, in recent studies, it was found that children aged 6 and 10 years, describing abstract shapes, showed evidence of face-to-face interference rather than facilitation. For some communication tasks, access to visual signals (such as facial expression and eye gaze) may hinder rather than help children’s communication. In new research we have pursued this interference effect. Five studies are described with adults and 10- and 6-year-old participants. It was found that looking at a face interfered with children’s abilities to listen to descriptions of abstract shapes. Children also performed visuospatial memory tasks worse when they looked at someone’s face prior to responding than when they looked at a visuospatial pattern or at the floor. It was concluded that performance on certain tasks was hindered by monitoring another person’s face. It is suggested that processing of visual communication signals shares certain processing resources with the processing of other visuospatial information
Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations
Coherent state theory is shown to reproduce three categories of
representations of the spectrum generating algebra for an algebraic model: (i)
classical realizations which are the starting point for geometric quantization;
(ii) induced unitary representations corresponding to prequantization; and
(iii) irreducible unitary representations obtained in geometric quantization by
choice of a polarization. These representations establish an intimate relation
between coherent state theory and geometric quantization in the context of
induced representations.Comment: 29 pages, part 1 of two papers, published versio
Nonlocal looking equations can make nonlinear quantum dynamics local
A general method for extending a non-dissipative nonlinear Schr\"odinger and
Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles
is described. It is shown at a general level that the dynamics so obtained is
completely separable, which is the strongest condition one can impose on
dynamics of composite systems. It requires that for all initial states
(entangled or not) a subsystem not only cannot be influenced by any action
undertaken by an observer in a separated system (strong separability), but
additionally that the self-consistency condition is fulfilled. It is shown that a correct
extension to particles involves integro-differential equations which, in
spite of their nonlocal appearance, make the theory fully local. As a
consequence a much larger class of nonlinearities satisfying the complete
separability condition is allowed than has been assumed so far. In particular
all nonlinearities of the form are acceptable. This shows that
the locality condition does not single out logarithmic or 1-homeogeneous
nonlinearities.Comment: revtex, final version, accepted in Phys.Rev.A (June 1998
New CMB Power Spectrum Constraints from MSAMI
We present new cosmic microwave background (CMB) anisotropy results from the
combined analysis of the three flights of the first Medium Scale Anisotropy
Measurement (MSAM1). This balloon-borne bolometric instrument measured about 10
square degrees of sky at half-degree resolution in 4 frequency bands from 5.2
icm to 20 icm with a high signal-to-noise ratio. Here we present an overview of
our analysis methods, compare the results from the three flights, derive new
constraints on the CMB power spectrum from the combined data and reduce the
data to total-power Wiener-filtered maps of the CMB. A key feature of this new
analysis is a determination of the amplitude of CMB fluctuations at . The analysis technique is described in a companion paper by Knox.Comment: 9 pages, 6 included figure
- …