1,411 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
The 21-cm Background from the Cosmic Dark Ages: Minihalos and the Intergalactic Medium before Reionization
The H atoms inside minihalos (i.e. halos with virial temperatures T_vir <
10^4 K, in the mass range roughly from 10^4 M_sun to 10^8 M_sun) during the
cosmic dark ages in a LCDM universe produce a redshifted background of
collisionally-pumped 21-cm line radiation which can be seen in emission
relative to the cosmic microwave background (CMB). Previously, we used
semi-analytical calculations of the 21-cm signal from individual halos of
different mass and redshift and the evolving mass function of minihalos to
predict the mean brightness temperature of this 21-cm background and its
angular fluctuations. Here we use high-resolution cosmological N-body and
hydrodynamic simulations of structure formation at high redshift (z > 8) to
compute the mean brightness temperature of this background from both minihalos
and the intergalactic medium (IGM) prior to the onset of Ly-alpha radiative
pumping. We find that the 21-cm signal from gas in collapsed, virialized
minihalos dominates over that from the diffuse shocked gas in the IGM.Comment: 8 pages, 5 figures. To appear in proceedings of UC Irvine May 2005
workshop on "First Light & Reionization", eds. E. Barton & A. Cooray, New
Astronomy Reviews, in pres
Fibre bundle formulation of nonrelativistic quantum mechanics. 0. Preliminary considerations: Quantum mechanics from a geometric-observer's viewpoint
We propose a version of the non-relativistic quantum mechanics in which the
pure states of a quantum system are described as sections of a Hilbert
(generally infinitely-dimensional) fibre bundle over the space-time. There
evolution is governed via (a kind of) a parallel transport in this bundle. Some
problems concerning observables are considered. There are derived the equations
of motion for the state sections and observables. We show that up to a constant
the matrix of the coefficients of the evolution operator (transport) coincides
with the matrix of the Hamiltonian of the investigated quantum system.Comment: 15 standard LaTeX 2e (11pt, A4) pages. The packages AMS-LaTeX and
amsfonts are require
The Abel-Jacobi map for a cubic threefold and periods of Fano threefolds of degree 14
The Abel-Jacobi maps of the families of elliptic quintics and rational
quartics lying on a smooth cubic threefold are studied. It is proved that their
generic fiber is the 5-dimensional projective space for quintics, and a smooth
3-dimensional variety birational to the cubic itself for quartics. The paper is
a continuation of the recent work of Markushevich-Tikhomirov, who showed that
the first Abel-Jacobi map factors through the moduli component of stable rank 2
vector bundles on the cubic threefold with Chern numbers
obtained by Serre's construction from elliptic quintics, and that the
factorizing map from the moduli space to the intermediate Jacobian is \'etale.
The above result implies that the degree of the \'etale map is 1, hence the
moduli component of vector bundles is birational to the intermediate Jacobian.
As an applicaton, it is shown that the generic fiber of the period map of Fano
varieties of degree 14 is birational to the intermediate Jacobian of the
associated cubic threefold.Comment: Latex, 28 page
Fibre bundle formulation of relativistic quantum mechanics. I. Time-dependent approach
We propose a new fibre bundle formulation of the mathematical base of
relativistic quantum mechanics. At the present stage the bundle form of the
theory is equivalent to its conventional one, but it admits new types of
generalizations in different directions.
In the present first part of our investigation we consider the time-dependent
or Hamiltonian approach to bundle description of relativistic quantum
mechanics. In it the wavefunctions are replaced by (state) liftings of paths or
sections along paths of a suitably chosen vector bundle over space-time whose
(standard) fibre is the space of the wavefunctions. Now the quantum evolution
is described as a linear transportation (by means of the evolution transport
along paths in the space-time) of the state liftings/sections in the (total)
bundle space. The equations of these transportations turn to be the bundle
versions of the corresponding relativistic wave equations.Comment: 16 standard LaTeX pages. The packages AMS-LaTeX and amsfonts are
required. The paper continuous the application of fibre bundle formalism to
quantum physics began in the series of works quant-ph/9803083,
quant-ph/9803084, quant-ph/9804062, quant-ph/9806046, quant-ph/9901039,
quant-ph/9902068, and quant-ph/0004041. For related papers, view
http://theo.inrne.bas.bg/~bozho
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
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