1,024 research outputs found
Fibre bundle formulation of nonrelativistic quantum mechanics. III. Pictures and integrals of motion
We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. It's evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
In this third part of our series we investigate the bundle analogues of the
conventional pictures of motion. In particular, there are found the state
sections and bundle morphisms corresponding to state vectors and observables
respectively. The equations of motion for these quantities are derived too.
Using the results obtained, we consider from the bundle view-point problems
concerning the integrals of motion. An invariant (bundle) necessary and
sufficient conditions for a dynamical variable to be an integral of motion are
found.Comment: 19 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and
amsfonts are required. New references and comments are added. Minor style
chages. Continuation of quant-ph/9803083, quant-ph/9803084 and
quant-ph/9804062. For continuation of the series view
http://www.inrne.bas.bg/mathmod/bozhome
Normal frames and the validity of the equivalence principle. III. The case along smooth maps with separable points of self-intersection
The equivalence principle is treated on a mathematically rigorous base on
sufficiently general subsets of a differentiable manifold. This is carried out
using the basis of derivations of the tensor algebra over that manifold.
Necessary and/or sufficient conditions of existence, uniqueness, and
holonomicity of these bases in which the components of the derivations of the
tensor algebra over it vanish on these subsets, are studied. The linear
connections are considered in this context. It is shown that the equivalence
principle is identically valid at any point, and along any path, in every
gravitational theory based on linear connections. On higher dimensional
submanifolds it may be valid only in certain exceptional cases.Comment: 15 standard LaTeX 2e (11pt, A4) pages. The package amsfonts is
require
Normal frames and the validity of the equivalence principle
We investigate the validity of the equivalence principle along paths in
gravitational theories based on derivations of the tensor algebra over a
differentiable manifold. We prove the existence of local bases, called normal,
in which the components of the derivations vanish along arbitrary paths. All
such bases are explicitly described. The holonomicity of the normal bases is
considered. The results obtained are applied to the important case of linear
connections and their relationship with the equivalence principle is described.
In particular, any gravitational theory based on tensor derivations which obeys
the equivalence principle along all paths, must be based on a linear
connection.Comment: 14 pages, LaTeX 2e, the package amsfonts is neede
Solitons and Almost-Intertwining Matrices
We define the set of almost-intertwining matrices to be all triples(X,Y,Z) of
n x n matrices for which XZ=YX+T for some rank one matrix T. A surprisingly
simple formula is given for tau-functions of the KP hierarchy in terms of such
triples. The tau-functions produced in this way include the soliton and
vanishing rational solutions. The induced dynamics of the eigenvalues of the
matrix X are considered, leading in special cases to the Ruijsenaars-Schneider
particle system
Auto-parallel equation as Euler-Lagrange's equation in spaces with affine connections and metrics
The auto-parallel equation over spaces with affine connections and metrics is
considered as a result of the application of the method of Lagrangians with
covariant derivatives (MLCD) on a given Lagrangian density.Comment: 19 pages, LaTe
Reionization: Characteristic Scales, Topology and Observability
Recently the numerical simulations of the process of reionization of the
universe at z>6 have made a qualitative leap forward, reaching sufficient sizes
and dynamic range to determine the characteristic scales of this process. This
allowed making the first realistic predictions for a variety of observational
signatures. We discuss recent results from large-scale radiative transfer and
structure formation simulations on the observability of high-redshift Ly-alpha
sources. We also briefly discuss the dependence of the characteristic scales
and topology of the ionized and neutral patches on the reionization parameters.Comment: 4 pages, 5 figures (4 in color), to appear in Astronomy and Space
Science special issue "Space Astronomy: The UV window to the Universe",
proceedings of 1st NUVA Conference ``Space Astronomy: The UV window to the
Universe'' in El Escorial (Spain
Frames of reference in spaces with affine connections and metrics
A generalized definition of a frame of reference in spaces with affine
connections and metrics is proposed based on the set of the following
differential-geometric objects:
(a) a non-null (non-isotropic) vector field,
(b) the orthogonal to the vector field sub space,
(c) an affine connection and the related to it covariant differential
operator determining a transport along the given non-null vector filed.
On the grounds of this definition other definitions related to the notions of
accelerated, inertial, proper accelerated and proper inertial frames of
reference are introduced and applied to some mathematical models for the
space-time. The auto-parallel equation is obtained as an Euler-Lagrange's
equation. Einstein's theory of gravitation appears as a theory for
determination of a special frame of reference (with the gravitational force as
inertial force) by means of the metrics and the characteristics of a material
distribution.
PACS numbers: 0490, 0450, 1210G, 0240VComment: 17 pages, LaTeX 2
Raman and Infrared-Active Phonons in Hexagonal HoMnO Single Crystals: Magnetic Ordering Effects
Polarized Raman scattering and infrared reflection spectra of hexagonal
HoMnO single crystals in the temperature range 10-300 K are reported.
Group-theoretical analysis is performed and scattering selection rules for the
second order scattering processes are presented. Based on the results of
lattice dynamics calculations, performed within the shell model, the observed
lines in the spectra are assigned to definite lattice vibrations. The magnetic
ordering of Mn ions, which occurs below T=76 K, is shown to effect both
Raman- and infrared-active phonons, which modulate Mn-O-Mn bonds and,
consequently, Mn exchange interaction.Comment: 8 pages, 6 figure
Flows and particles with shear-free and expansion-free velocities in (L^-_n,g)- and Weyl's spaces
Conditions for the existence of flows with non-null shear-free and
expansion-free velocities in spaces with affine connections and metrics are
found. On their basis, generalized Weyl's spaces with shear-free and
expansion-free conformal Killing vectors as velocity's vectors of spinless test
particles moving in a Weyl's space are considered. The necessary and sufficient
conditions are found under which a free spinless test particle could move in
spaces with affine connections and metrics on a curve described by means of an
auto-parallel equation. In Weyl's spaces with Weyl's covector, constructed by
the use of a dilaton field, the dilaton field appears as a scaling factor for
the rest mass density of the test particle. PACS numbers: 02.40.Ky, 04.20.Cv,
04.50.+h, 04.90.+eComment: 20 pages, LaTeX, to appear in Classical and Quantum Gravity. arXiv
admin note: substantial text overlap with arXiv:gr-qc/001104
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