8,353 research outputs found
Right eigenvalue equation in quaternionic quantum mechanics
We study the right eigenvalue equation for quaternionic and complex linear
matrix operators defined in n-dimensional quaternionic vector spaces. For
quaternionic linear operators the eigenvalue spectrum consists of n complex
values. For these operators we give a necessary and sufficient condition for
the diagonalization of their quaternionic matrix representations. Our
discussion is also extended to complex linear operators, whose spectrum is
characterized by 2n complex eigenvalues. We show that a consistent analysis of
the eigenvalue problem for complex linear operators requires the choice of a
complex geometry in defining inner products. Finally, we introduce some
examples of the left eigenvalue equations and highlight the main difficulties
in their solution.Comment: 24 pages, AMS-Te
Quaternionic potentials in non-relativistic quantum mechanics
We discuss the Schrodinger equation in presence of quaternionic potentials.
The study is performed analytically as long as it proves possible, when not, we
resort to numerical calculations. The results obtained could be useful to
investigate an underlying quaternionic quantum dynamics in particle physics.
Experimental tests and proposals to observe quaternionic quantum effects by
neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te
Quaternionic Electroweak Theory
We explicitly develop a quaternionic version of the electroweak theory, based
on the local gauge group . The need of a complex
projection for our Lagrangian and the physical significance of the anomalous
scalar solutions are also discussed.Comment: 12 pages, Revtex, submitted to J. Phys.
Quaternionic Electroweak Theory and CKM Matrix
We find in our quaternionic version of the electroweak theory an apparently
hopeless problem: In going from complex to quaternions, the calculation of the
real-valued parameters of the CKM matrix drastically changes. We aim to explain
this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published
An Analytic Approach to the Wave Packet Formalism in Oscillation Phenomena
We introduce an approximation scheme to perform an analytic study of the
oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian
wave packets, we show that the oscillation is bounded by a time-dependent
vanishing function which characterizes the slippage between the mass-eigenstate
wave packets. We also demonstrate that the wave packet spreading represents a
secondary effect which plays a significant role only in the non-relativistic
limit. In our analysis, we note the presence of a new time-dependent phase and
calculate how this additional term modifies the oscillating character of the
flavor conversion formula. Finally, by considering Box and Sine wave packets we
study how the choice of different functions to describe the particle
localization changes the oscillation probability.Comment: 16 pages, 7 figures, AMS-Te
A Smooth Lattice construction of the Oppenheimer-Snyder spacetime
We present test results for the smooth lattice method using an
Oppenheimer-Snyder spacetime. The results are in excellent agreement with
theory and numerical results from other authors.Comment: 60 pages, 28 figure
Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics
A suitable parameterization of space-time in terms of one complex and three
quaternionic imaginary units allows Lorentz transformations to be implemented
as multiplication by complex-quaternionic numbers rather than matrices.
Maxwell's equations reduce to a single equation.Comment: 8 page
Structure of Turbulence in Katabatic Flows below and above the Wind-Speed Maximum
Measurements of small-scale turbulence made over the complex-terrain
atmospheric boundary layer during the MATERHORN Program are used to describe
the structure of turbulence in katabatic flows. Turbulent and mean
meteorological data were continuously measured at multiple levels at four
towers deployed along the East lower slope (2-4 deg) of Granite Mountain. The
multi-level observations made during a 30-day long MATERHORN-Fall field
campaign in September-October 2012 allowed studying of temporal and spatial
structure of katabatic flows in detail, and herein we report turbulence and
their variations in katabatic winds. Observed vertical profiles show steep
gradients near the surface, but in the layer above the slope jet the vertical
variability is smaller. It is found that the vertical (normal to the slope)
momentum flux and horizontal (along the slope) heat flux in a slope-following
coordinate system change their sign below and above the wind maximum of a
katabatic flow. The vertical momentum flux is directed downward (upward)
whereas the horizontal heat flux is downslope (upslope) below (above) the wind
maximum. Our study therefore suggests that the position of the jet-speed
maximum can be obtained by linear interpolation between positive and negative
values of the momentum flux (or the horizontal heat flux) to derive the height
where flux becomes zero. It is shown that the standard deviations of all wind
speed components (therefore the turbulent kinetic energy) and the dissipation
rate of turbulent kinetic energy have a local minimum, whereas the standard
deviation of air temperature has an absolute maximum at the height of
wind-speed maximum. We report several cases where the vertical and horizontal
heat fluxes are compensated. Turbulence above the wind-speed maximum is
decoupled from the surface, and follows the classical local z-less predictions
for stably stratified boundary layer.Comment: Manuscript submitted to Boundary-Layer Meteorology (05 December 2014
Masses of a Fourth Generation with Two Higgs Doublets
We use sampling techniques to find robust constraints on the masses of a
possible fourth sequential fermion generation from electroweak oblique
variables. We find that in the case of a light (115 GeV) Higgs from a single
electroweak symmetry breaking doublet, inverted mass hierarchies are possible
for both quarks and leptons, but a mass splitting more than M(W) in the quark
sector is unlikely. We also find constraints in the case of a heavy (600 GeV)
Higgs in a single doublet model. As recent data from the Large Hadron Collider
hints at the existence of a resonance at 124.5 GeV and a single Higgs doublet
at that mass is inconsistent with a fourth fermion generation, we examine a
type II two Higgs doublet model. In this model, there are ranges of parameter
space where the Higgs sector can potentially counteract the effects of the
fourth generation. Even so, we find that such scenarios produce qualitatively
similar fermion mass distributions.Comment: v2: 9 pages, 7 figures, improved analysis of Higgs decay constraints,
typos corrected and reference adde
- …