4,421 research outputs found
Discrete Symmetries of Off-Shell Electromagnetism
We discuss the discrete symmetries of the Stueckelberg-Schrodinger
relativistic quantum theory and its associated 5D local gauge theory, a
dynamical description of particle/antiparticle interactions, with monotonically
increasing Poincare-invariant parameter. In this framework, worldlines are
traced out through the parameterized evolution of spacetime events, advancing
or retreating with respect to the laboratory clock, with negative energy
trajectories appearing as antiparticles when the observer describes the
evolution using the laboratory clock. The associated gauge theory describes
local interactions between events (correlated by the invariant parameter)
mediated by five off-shell gauge fields. These gauge fields are shown to
transform tensorially under under space and time reflections, unlike the
standard Maxwell fields, and the interacting quantum theory therefore remains
manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory
is achieved by simultaneous reflection of the sense of evolution and the fifth
scalar field. Applying this procedure to the classical gauge theory leads to a
purely classical manifestation of charge conjugation, placing the CPT
symmetries on the same footing in the classical and quantum domains. In the
resulting picture, interactions do not distinguish between particle and
antiparticle trajectories -- charge conjugation merely describes the
interpretation of observed negative energy trajectories according to the
laboratory clock.Comment: 26 page
Eikonal Approximation to 5D Wave Equations as Geodesic Motion in a Curved 4D Spacetime
We first derive the relation between the eikonal approximation to the Maxwell
wave equations in an inhomogeneous anisotropic medium and geodesic motion in a
three dimensional Riemannian manifold using a method which identifies the
symplectic structure of the corresponding mechanics. We then apply an analogous
method to the five dimensional generalization of Maxwell theory required by the
gauge invariance of Stueckelberg's covariant classical and quantum dynamics to
demonstrate, in the eikonal approximation, the existence of geodesic motion for
the flow of mass in a four dimensional pseudo-Riemannian manifold. These
results provide a foundation for the geometrical optics of the five dimensional
radiation theory and establish a model in which there is mass flow along
geodesics. Finally we discuss the case of relativistic quantum theory in an
anisotropic medium as well. In this case the eikonal approximation to the
relativistic quantum mechanical current coincides with the geodesic flow
governed by the pseudo-Riemannian metric obtained from the eikonal
approximation to solutions of the Stueckelberg-Schr\"odinger equation. This
construction provides a model for an underlying quantum mechanical structure
for classical dynamical motion along geodesics on a pseudo-Riemannian manifold.
The locally symplectic structure which emerges is that of Stueckelberg's
covariant mechanics on this manifold.Comment: TeX file. 17 pages. Rewritten for clarit
Engaging and empowering first-year students through curriculum design: perspectives from the literature
There is an increasing value being placed on engaging and empowering first-year students and first-year curriculum design is a key driver and opportunity to ensure early enculturation into successful learning at university. This paper summarises the literature on first-year curriculum design linked to student engagement and empowerment. We present conceptualisations of ‘curriculum’ and examples from first-year curriculum design. We also note the limited literature where students have been involved in designing first-year curricula. The results of the literature review suggest that key characteristics of engaging first-year curricula include active learning, timely feedback, relevance and challenge. The literature also points to the importance of identifying students' abilities on entry to university as well as being clear about desired graduate attributes and developmental goals. Acknowledging realities and constraints, we present a framework for the first-year curriculum design process based on the literature
Footprints of Statistical Anisotropies
We propose and develop a formalism to describe and constrain statistically
anisotropic primordial perturbations. Starting from a decomposition of the
primordial power spectrum in spherical harmonics, we find how the temperature
fluctuations observed in the CMB sky are directly related to the coefficients
in this harmonic expansion. Although the angular power spectrum does not
discriminate between statistically isotropic and anisotropic perturbations, it
is possible to define analogous quadratic estimators that are direct measures
of statistical anisotropy. As a simple illustration of our formalism we test
for the existence of a preferred direction in the primordial perturbations
using full-sky CMB maps. We do not find significant evidence supporting the
existence of a dipole component in the primordial spectrum.Comment: 26 pages, 5 double figures. Uses RevTeX
Lamb Wave Modes in Coal-Tar-Coated Steel Plates
In order to study the feasibility of using ultrasonic Lamb wave modes for detection and sizing of corrosion-related flaws in buried steel pipelines, we have calculated Lamb wave modes and performed numerous experiments on steel plates coated on one side with coal-tar enamel. The purpose of this paper is to discuss these theoretical and experimental results
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