946 research outputs found
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
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
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
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
Simulating the Impact of X-ray Heating during the Cosmic Dawn
Upcoming observations of the 21-cm signal from the Epoch of Reionization will
soon provide the first direct detection of this era. This signal is influenced
by many astrophysical effects, including long range X-ray heating of the
intergalactic gas. During the preceding Cosmic Dawn era the impact of this
heating on the 21-cm signal is particularly prominent, especially before spin
temperature saturation. We present the largest-volume (349\,Mpc
comoving=244~Mpc) full numerical radiative transfer simulations to date
of this epoch that include the effects of helium and multi-frequency heating,
both with and without X-ray sources. We show that X-ray sources contribute
significantly to early heating of the neutral intergalactic medium and, hence,
to the corresponding 21-cm signal. The inclusion of hard, energetic radiation
yields an earlier, extended transition from absorption to emission compared to
the stellar-only case. The presence of X-ray sources decreases the absolute
value of the mean 21-cm differential brightness temperature. These hard sources
also significantly increase the 21-cm fluctuations compared the common
assumption of temperature saturation. The 21-cm differential brightness
temperature power spectrum is initially boosted on large scales, before
decreasing on all scales. Compared to the case of the cold, unheated
intergalactic medium, the signal has lower rms fluctuations and increased
non-Gaussianity, as measured by the skewness and kurtosis of the 21-cm
probability distribution functions. Images of the 21-cm signal with resolution
around 11~arcmin still show fluctuations well above the expected noise for deep
integrations with the SKA1-Low, indicating that direct imaging of the X-ray
heating epoch could be feasible.Comment: 13 pages, 8 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
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
A Physical Model of Lyman Alpha Emitters
We present a simple physical model for populating dark matter halos with
Lyman Alpha Emiiters(LAEs) and predict the physical properties of LAEs at
z~3-7. The central tenet of this model is that the Ly-alpha luminosity is
proportional to the star formation rate (SFR) which is directly related to the
halo mass accretion rate. The only free parameter in our model is then the
star-formation efficiency (SFE). An efficiency of 2.5% provides the best-fit to
the Ly-alpha luminosity function (LF) at redshift z=3.1, and we use this SFE to
construct Ly-alpha LFs at other redshifts. Our model reproduce the Ly-alpha
LFs, stellar ages, SFR ~1-10; Msun/yr, stellar masses ~ 10^7-10^8 Msun and the
clustering properties of LAEs at z~3-7. We find the spatial correlation lengths
ro ~ 3-6 Mpc/h, in agreement with the observations. Finally, we estimate the
field-to-field variation ~ 30% for current volume and flux limited surveys,
again consistent with observations. Our results suggest that the star
formation, and hence Ly-alpha emission in LAEs is powered by the accretion of
new material, and that the physical properties of LAEs do not evolve
significantly over a wide range of redshifts. Relating the accreted mass,
rather than the total mass of halos, to the Ly-alpha luminosity of LAEs
naturally gives rise to the duty cycle of LAEs.Comment: Published in Ap
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