1,962 research outputs found
Action Principle for the Generalized Harmonic Formulation of General Relativity
An action principle for the generalized harmonic formulation of general
relativity is presented. The action is a functional of the spacetime metric and
the gauge source vector. An action principle for the Z4 formulation of general
relativity has been proposed recently by Bona, Bona--Casas and Palenzuela
(BBP). The relationship between the generalized harmonic action and the BBP
action is discussed in detail.Comment: This version is contains more thorough presentations and discussions
of the key results. To be published in PRD. (8 pages, no figures
A very brief introduction to quantum computing and quantum information theory for mathematicians
This is a very brief introduction to quantum computing and quantum
information theory, primarily aimed at geometers. Beyond basic definitions and
examples, I emphasize aspects of interest to geometers, especially connections
with asymptotic representation theory. Proofs of most statements can be found
in standard references
Einstein's fluctuation formula. A historical overview
A historical overview is given on the basic results which appeared by the
year 1926 concerning Einstein's fluctuation formula of black-body radiation, in
the context of light-quanta and wave-particle duality. On the basis of the
original publications (from Planck's derivation of the black-body spectrum and
Einstein's introduction of the photons up to the results of Born, Heisenberg
and Jordan on the quantization of a continuum) a comparative study is presented
on the first line of thoughts that led to the concept of quanta. The nature of
the particle-like fluctuations and the wave-like fluctuations are analysed by
using several approaches. With the help of the classical probability theory, it
is shown that the infinite divisibility of the Bose distribution leads to the
new concept of classical poissonian photo-multiplets or to the binary
photo-multiplets of fermionic character. As an application, Einstein's
fluctuation formula is derived as a sum of fermion type fluctuations of the
binary photo-multiplets.Comment: 34 page
On the Foundation of the Relativistic Dynamics with the Tachyon
The theoretical foundation of the object moving faster than light in vacuum
({\it tachyon}) is still missing or incomplete. Here we present the classical
foundation of the relativistic dynamics including the tachyon. An anomalous
sign-factor extracted from the transformation of
under the Lorentz transformation, which has been always missed in the usual
formulation of the tachyon, has a crucial role in the dynamics of the tachyon.
Due to this factor the mass of the tachyon transforms in the unusual way
although the energy and momentum, which are defined as the conserved quantities
in all uniformly moving systems, transform in the usual way as in the case of
the object moving slower than light ({\it bradyon}). We show that this result
can be also obtained from the least action approach. On the other hand, we show
that the ambiguities for the description of the dynamics for the object moving
with the velocity of light ({\it luxon}) can be consistently removed only by
introducing a new dynamical variable. Furthermore, by using the fundamental
definition of the momentum and energy we show that the zero-point energy for
any kind of the objects, {\it i.e.}, the tachyon, bradyon, and luxon, which has
been known as the undetermined constant, should satisfy some constraints for
consistency, and we note that this is essentially another novel relativistic
effect. Finally, we remark about the several unsolved problems.Comment: 39 pages, latex, 15 figures avaliable upon reques
Accelerating Universe as Window for Extra Dimensions
Homogeneous cosmological solutions are obtained in five dimensional space
time assuming equations of state and where p
is the isotropic 3 - pressure and , that for the fifth dimension. Using
different values for the constants k and many known solutions are
rediscovered. Further the current acceleration of the universe has led us to
investigate higher dimensional gravity theory, which is able to explain
acceleration from a theoretical view point without the need of introducing dark
energy by hand. We argue that the terms containing higher dimensional metric
coefficients produce an extra negative pressure that apparently drives an
acceleration of the 3D space, tempting us to suggest that the accelerating
universe seems to act as a window to the existence of extra spatial dimensions.
Interestingly the 5D matter field remains regular while the \emph{effective}
negative pressure is responsible for the inflation. Relaxing the assumptions of
two equations of state we also present a class of solutions which provide early
deceleration followed by a late acceleration in a unified manner. Interesting
to point out that in this case our cosmology apparently mimics the well known
quintessence scenario fuelled by a generalised Chaplygin-type of fluid where a
smooth transition from a dust dominated model to a de Sitter like one takes
place.Comment: 20 pages,3 figure
Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics
In this article, we analyze the third of three papers, in which Einstein
presented his quantum theory of the ideal gas of 1924-1925. Although it failed
to attract the attention of Einstein's contemporaries and although also today
very few commentators refer to it, we argue for its significance in the context
of Einstein's quantum researches. It contains an attempt to extend and exhaust
the characterization of the monatomic ideal gas without appealing to
combinatorics. Its ambiguities illustrate Einstein's confusion with his initial
success in extending Bose's results and in realizing the consequences of what
later became to be called Bose-Einstein statistics. We discuss Einstein's
motivation for writing a non-combinatorial paper, partly in response to
criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments
are based on Einstein's belief in the complete analogy between the
thermodynamics of light quanta and of material particles and invoke
considerations of adiabatic transformations as well as of dimensional analysis.
These techniques were well-known to Einstein from earlier work on Wien's
displacement law, Planck's radiation theory, and the specific heat of solids.
We also investigate the possible role of Ehrenfest in the gestation of the
theory.Comment: 57 pp
Gravity, p-branes and a spacetime counterpart of the Higgs effect
We point out that the worldvolume coordinate functions of
a -brane, treated as an independent object interacting with dynamical
gravity, are Goldstone fields for spacetime diffeomorphisms gauge symmetry. The
presence of this gauge invariance is exhibited by its associated Noether
identity, which expresses that the source equations follow from the
gravitational equations. We discuss the spacetime counterpart of the Higgs
effect and show that a -brane does not carry any local degrees of freedom,
extending early known general relativity features. Our considerations are also
relevant for brane world scenarios.Comment: 5 pages, RevTeX. v2 (30-IV-03) with additional text and reference
Implication of the overlap representation for modelling generalized parton distributions
Based on a field theoretically inspired model of light-cone wave functions,
we derive valence-like generalized parton distributions and their double
distributions from the wave function overlap in the parton number conserved
s-channel. The parton number changing contributions in the t-channel are
restored from duality. In our construction constraints of positivity and
polynomiality are simultaneously satisfied and it also implies a model
dependent relation between generalized parton distributions and transverse
momentum dependent parton distribution functions. The model predicts that the
t-behavior of resulting hadronic amplitudes depends on the Bjorken variable
x_Bj. We also propose an improved ansatz for double distributions that embeds
this property.Comment: 15 pages, 8 eps figure
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