pinecone/core-2020-05-10-deduplication huggingface dataset:
Massive Supersymmetric Quantum Gauge Theory

We continue the study of the supersymmetric vector multiplet in a purely
quantum framework. We obtain some new results which make the connection with
the standard literature. First we construct the one-dimensional physical
Hilbert space taking into account the (quantum) gauge structure of the model.
Then we impose the condition of positivity for the scalar product only on the
physical Hilbert space. Finally we obtain a full supersymmetric coupling which
is gauge invariant in the supersymmetric sense in the first order of
perturbation theory. By integrating out the Grassmann variables we get an
interacting Lagrangian for a massive Yang-Mills theory related to ordinary
gauge theory; however the number of ghost fields is doubled so we do not obtain
the same ghost couplings as in the standard model Lagrangian.Comment: 13 pages, no figure
Non-relativistic quantum scattering from non-local separable potentials:
  the eigenchannel approach

A recently formulated version of the eigenchannel method [R. Szmytkowski,
Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] is applied to quantum scattering of
Schr\"odinger particles from non-local separable potentials. Eigenchannel
vectors and negative cotangents of eigenphase-shifts are introduced as
eigensolutions to some weighted matrix spectral problem, without a necessity of
prior construction and diagonalization of the scattering matrix. Explicit
expressions for the scattering amplitude, the total cross section in terms of
the eigenchannel vectors and the eigenphase-shifts are derived. An illustrative
example is provided.Comment: 10 pages, slightly improved versio
Gravity and the Quantum Vacuum Inertia Hypothesis

In previous work it has been shown that the electromagnetic quantum vacuum,
or electromagnetic zero-point field, makes a contribution to the inertial
reaction force on an accelerated object. We show that the result for inertial
mass can be extended to passive gravitational mass. As a consequence the weak
equivalence principle, which equates inertial to passive gravitational mass,
appears to be explainable. This in turn leads to a straightforward derivation
of the classical Newtonian gravitational force. We call the inertia and
gravitation connection with the vacuum fields the quantum vacuum inertia
hypothesis. To date only the electromagnetic field has been considered. It
remains to extend the hypothesis to the effects of the vacuum fields of the
other interactions. We propose an idealized experiment involving a cavity
resonator which, in principle, would test the hypothesis for the simple case in
which only electromagnetic interactions are involved. This test also suggests a
basis for the free parameter $\eta(\nu)$ which we have previously defined to
parametrize the interaction between charge and the electromagnetic zero-point
field contributing to the inertial mass of a particle or object.Comment: 18 pages, no figures. Annalen der Physik, 2005, in press. New version
  reformatte
Non-Volkov solutions for a charge in a plane wave

We focus our attention, once again, on the Klein--Gordon and Dirac equations
with a plane-wave field. We recall that for the first time a set of solutions
of these equations was found by Volkov. The Volkov solutions are widely used in
calculations of quantum effects with electrons and other elementary particles
in laser beams. We demonstrate that one can construct sets of solutions which
differ from the Volkov solutions and which may be useful in physical
applications. For this purpose, we show that the transversal charge motion in a
plane wave can be mapped by a special transformation to transversal free
particle motion. This allows us to find new sets of solutions where the
transversal motion is characterized by quantum numbers different from Volkov's
(in the Volkov solutions this motion is characterized by the transversal
momentum). In particular, we construct solutions with semiclassical transversal
charge motion (transversal squeezed coherent states). In addition, we
demonstrate how the plane-wave field can be eliminated from the transversal
charge motion in a more complicated case of the so-called combined
electromagnetic field (a combination of a plane-wave field and constant
colinear electric and magnetic fields). Thus, we find new sets of solutions of
the Klein--Gordon and Dirac equations with the combined electromagnetic field.Comment: LaTex file, 14 page
Effective descriptions of complex quantum systems: path integrals and
  operator ordering problems

We study certain aspects of the effective, occasionally called collective,
description of complex quantum systems within the framework of the path
integral formalism, in which the environment is integrated out. Generalising
the standard Feynman-Vernon Caldeira-Leggett model to include a non-linear
coupling between ``particle'' and environment, and considering a particular
spectral density of the coupling, a coordinate-dependent mass (or
velocity-dependent potential) is obtained. The related effective quantum
theory, which depends on the proper discretisation of the path integral, is
derived and discussed. As a result, we find that in general a simple effective
low-energy Hamiltonian, in which only the coordinate-dependent mass enters,
cannot be formulated. The quantum theory of weakly coupled superconductors and
the quantum dynamics of vortices in Josephson junction arrays are physical
examples where these considerations, in principle, are of relevance.Comment: 13 pages, no figure
Green functions for nearest- and next-nearest-neighbor hopping on the
  Bethe lattice

We calculate the local Green function for a quantum-mechanical particle with
hopping between nearest and next-nearest neighbors on the Bethe lattice, where
the on-site energies may alternate on sublattices. For infinite connectivity
the renormalized perturbation expansion is carried out by counting all
non-self-intersecting paths, leading to an implicit equation for the local
Green function. By integrating out branches of the Bethe lattice the same
equation is obtained from a path integral approach for the partition function.
This also provides the local Green function for finite connectivity. Finally, a
recently developed topological approach is extended to derive an operator
identity which maps the problem onto the case of only nearest-neighbor hopping.
We find in particular that hopping between next-nearest neighbors leads to an
asymmetric spectrum with additional van-Hove singularities.Comment: 16 pages, 7 figures; minor change
Orbital order, anisotropic spin couplings, and the spin-wave spectrum of
  the ferromagnetic Mott insulator YTiO3

Using a point-charge calculation of the electrostatic crystal field, we
determine the non-degenerate orbital ground state of the ferromagnetic Mott
insulator YTiO3, which is found to agree perfectly with experiment. Based on
the orbital order, we obtain by perturbation theory an effective spin
Hamiltonian that describes the magnetic superexchange between nearest-neighbor
Ti ions. The superexchange Hamiltonian includes, in addition to the isotropic
Heisenberg coupling, antisymmetric (Dzyaloshinskii-Moriya) and symmetric
anisotropy terms, caused by the spin-orbit interaction on the Ti ions. We find
ferromagnetic Heisenberg couplings for Ti-Ti bonds in the crystallographic ab
planes, but antiferromagnetic ones for Ti-Ti bonds between planes, in
contradiction with experiment (which gives ferromagnetic couplings for both).
Difficulties in calculating realistic values for the isotropic couplings of
YTiO3 have been already reported in the literature. We discuss possible origins
for these discrepancies. However, the much smaller values we obtain for the
symmetric and antisymmetric anisotropies may be expected to be reliable. We
therefore combine the experimentally-deduced isotropic coupling with the
calculated anisotropic ones to determine the magnetic order of the Ti ions,
which is found to be in satisfactory agreement with experiment. Based on this
magnetic order, we derive the spin-wave spectrum. We find an acoustic branch
with a very small zone-center gap and three optical spin-wave modes with
sizeable zone-center gaps. The acoustic branch reproduces the one reported in
experiment, and the optical ones are in a satisfactory agreement with
experiment, upon a proper folding of the magnetic Brillouin zone.Comment: 13 pages, 5 figures, submitted to Ann. Phys. Leipzi
The gravitational energy-momentum tensor and the gravitational pressure

In the framework of the teleparallel equivalent of general relativity it is
possible to establish the energy-momentum tensor of the gravitational field.
This tensor has the following essential features: (1) it is identified directly
in Einstein's field equations; (2) it is conserved and traceless; (3) it yields
expressions for the energy and momentum of the gravitational field; (4)it is
free of second (and highest) derivatives of the field variables; (5) the
gravitational and matter energy-momentum tensors take place in the field
equations on the same footing; (6) it is unique. However, it is not symmetric.
We show that the spatial components of this tensor yield a consistent
definition of the gravitational pressure.Comment: 16 pages, Latex file. Two references added. Revised in view of
  Referee's comments. Accepted by Annalen der Physi
Was Einstein Right? Testing Relativity at the Centenary

We review the experimental evidence for Einstein's special and general
relativity. A variety of high precision null experiments verify the weak
equivalence principle and local Lorentz invariance, while gravitational
redshift and other clock experiments support local position invariance.
Together these results confirm the Einstein Equivalence Principle which
underlies the concept that gravitation is synonymous with spacetime geometry,
and must be described by a metric theory. Solar system experiments that test
the weak-field, post-Newtonian limit of metric theories strongly favor general
relativity. The Binary Pulsar provides tests of gravitational-wave damping and
of strong-field general relativity. Recently discovered binary pulsar systems
may provide additional tests. Future and ongoing experiments, such as the
Gravity Probe B Gyroscope Experiment, satellite tests of the Equivalence
principle, and tests of gravity at short distance to look for extra spatial
dimensions could constrain extensions of general relativity. Laser
interferometric gravitational-wave observatories on Earth and in space may
provide new tests of gravitational theory via detailed measurements of the
properties of gravitational waves.Comment: 21 pages, 3 figures, to be published in "100 Years of Relativity:
  Spacetime Structure - Einstein and Beyond", ed. Abhay Ashtekar (World
  Scientific, Singapore
Is general relativity `essentially understood' ?

The content of Einstein's theory of gravitation is encoded in the properties
of the solutions to his field equations. There has been obtained a wealth of
information about these solutions in the ninety years the theory has been
around. It led to the prediction and the observation of physical phenomena
which confirm the important role of general relativity in physics. The
understanding of the domain of highly dynamical, strong field configurations
is, however, still quite limited. The gravitational wave experiments are likely
to provide soon observational data on phenomena which are not accessible by
other means. Further theoretical progress will require, however, new methods
for the analysis and the numerical calculation of the solutions to Einstein's
field equations on large scales and under general assumptions. We discuss some
of the problems involved, describe the status of the field and recent results,
and point out some open problems.Comment: Extended version of a talk which was to be delivered at the DPG
  Fruehjahrstagung in Berlin, 5 March 200
Quantum Gravity: General Introduction and Recent Developments

I briefly review the current status of quantum gravity. After giving some
general motivations for the need of such a theory, I discuss the main
approaches in quantizing general relativity: Covariant approaches (perturbation
theory, effective theory, and path integrals) and canonical approaches (quantum
geometrodynamics, loop quantum gravity). I then address quantum gravitational
aspects of string theory. This is followed by a discussion of black holes and
quantum cosmology. I end with some remarks on the observational status of
quantum gravity.Comment: 21 pages, 6 figures, invited contribution for "Annalen der Physik",
  v2: minor corrections, additional reference
Spin equation and its solutions

The aim of the present article is to study in detail the so-called spin
equation (SE) and present both the methods of generating new solution and a new
set of exact solutions. We recall that the SE with a real external field can be
treated as a reduction of the Pauli equation to the (0+1)-dimensional case.
Two-level systems can be described by an SE with a particular form of the
external field. In this article, we also consider associated equations that are
equivalent or (in one way or another) related to the SE. We describe the
general solution of the SE and solve the inverse problem for this equation. We
construct the evolution operator for the SE and consider methods of generating
new sets of exact solutions. Finally, we find a new set of exact solutions of
the SE.Comment: 29 page
Koopman-von Neumann Formulation of Classical Yang-Mills Theories: I

In this paper we present the Koopman-von Neumann (KvN) formulation of
classical non-Abelian gauge field theories. In particular we shall explore the
functional (or classical path integral) counterpart of the KvN method. In the
quantum path integral quantization of Yang-Mills theories concepts like
gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We
will prove that these same objects are needed also in this classical path
integral formulation for Yang-Mills theories. We shall also explore the
classical path integral counterpart of the BFV formalism and build all the
associated universal and gauge charges. These last are quite different from the
analog quantum ones and we shall show the relation between the two. This paper
lays the foundation of this formalism which, due to the many auxiliary fields
present, is rather heavy. Applications to specific topics outlined in the paper
will appear in later publications.Comment: 46 pages, Late
No cross-interactions between the Weyl graviton and the massless
  Rarita-Schwinger field

The proof of the fact that there are no nontrivial, consistent
cross-couplings that can be added between the Weyl graviton and the massless
Rarita-Schwinger field is accomplished by means of a cohomological approach,
based on the deformation of the solution to the master equation from the
antifield-Becchi-Rouet-Stora-Tyutin (BRST) formalism. The procedure developed
here relies on the assumptions of locality, smoothness, (background) Lorentz
invariance, Poincare invariance, and preservation of the number of derivatives
with respect to each field (the last hypothesis was made only in antighost
number zero).Comment: 26 page
Time evolution of relativistic d + Au and Au + Au collisions

The evolution of charged-particle production in collisions of heavy ions at
relativistic energies is investigated as function of centrality in a
nonequilibrium-statistical framework. Precise agreement with recent d + Au and
Au + Au data at sqrt(s_NN) = 200 GeV is found in a Relativistic Diffusion Model
with three sources for particle production. Only the midrapidity source comes
very close to local equilibrium, whereas the analyses of the overall
pseudorapidity distributions show that the systems remain far from statistical
equilibrium.Comment: 16 pages, 5 figures, 1 tabl
The Revival of Cosmic Strings

Cosmic strings are one-dimensional topological defects which could have been
formed in the early stages of our Universe. They triggered a lot of interest,
mainly for their cosmological implications: they could offer an alternative to
inflation for the generation of density perturbations. It was shown however
that cosmic strings lead to inconsistencies with the measurements of the cosmic
microwave background temperature anisotropies. The picture is changed recently.
It was shown that, on the one hand, cosmic strings can be generically formed in
the framework of supersymmetric grand unified theories and that, on the other
hand, cosmic superstrings could play the r\^ole of cosmic strings. There is
also some possible observational support. All this lead to a revival of cosmic
strings research and this is the topic of my lecture.Comment: 13 pages, Invited Lecture in " Pomeranian Workshop in Fundamental
  Cosmology" (Poland 2005), to be published in Annalen der Physi
Cosmologies from higher-order string corrections

We study cosmologies based on low-energy effective string theory with
higher-order string corrections to a tree-level action and with a modulus
scalar field (dilaton or compactification modulus). In the presence of such
corrections it is possible to construct nonsingular cosmological solutions in
the context of Pre-Big-Bang and Ekpyrotic universes. We review the construction
of nonsingular bouncing solutions and resulting density perturbations in
Pre-Big-Bang and Ekpyrotic models. We also discuss the effect of higher-order
string corrections on dark energy universe and show several interesting
possibilities of the avoidance of future singularities.Comment: 15 pages, 2 figures, References are added, plenary talk at Pomeranian
  Workshop in Fundamental Cosmology (COSMOFUN 05), Pobierowo, Poland, 1-6
  September 200
Electrodynamics of correlated electron matter

Infrared spectroscopy has emerged as a premier experimental technique to
probe enigmatic effects arising from strong correlations in solids. Here we
report on recent advances in this area focusing on common patterns in
correlated electron systems including transition metal oxides, intermetallics
and organic conductors. All these materials are highly conducting substances
but their electrodynamic response is profoundly different from the canonical
Drude behavior observed in simple metals. These unconventional properties can
be attributed in several cases to the formation of spin and/or charge ordered
states, zero temperature phase transitions and strong coupling to bosonic
modes
Dynamic conductivity of semiconducting manganites approaching the
  metal-insulator transition

We report the frequency-dependent conductivity of the manganite system
La1-xSrxMnO3 (x <= 0.2) when approaching the metal-insulator transition from
the insulating side. Results from low-frequency dielectric measurements are
combined with spectra in the infrared region. For low doping levels the
behavior is dominated by hopping transport of localized charge carriers at low
frequencies and by phononic and electronic excitations in the infrared region.
For the higher Sr contents the approach of the metallic state is accompanied by
the successive suppression of the hopping contribution at low frequencies and
by the development of polaronic excitations in the infrared region, which
finally become superimposed by a strong Drude contribution in the fully
metallic state.Comment: 10 pages, 7 figure
Optical Conductivity of Clean Metals

We briefly review some basic aspects of transport in clean metals focusing on
the role of electron-electron interactions and neglecting the effects of
impurities, phonons and interband transitions. Both for small Fermi surfaces of
two and three-dimensional metals and open Fermi surfaces of quasi
one-dimensional metals the dc conductivity sigma is largely dominated by
momentum and pseudo-momentum conservation, respectively. In general, the
frequency and temperature dependencies of sigma(w,T) have very little in
common. For small Fermi surfaces in three dimensions we find for example that
the scattering rate is quadratic in frequency, Gamma \propto w^2, even in the
absence of a T^2 contribution.Comment: invited paper for a special edition of Annalen der Physik
  commemorating P. Drud
Anomalous Hall effect in ferromagnetic disordered metals

The anomalous Hall effect in disordered band ferromagnets is considered in
the framework of quantum transport theory. A microscopic model of electrons in
a random potential of identical impurities including spin-orbit coupling is
used. The Hall conductivity is calculated from the Kubo formula for both, the
skew scattering and the side-jump mechanisms. The recently discussed Berry
phase induced Hall current is also evaluated within the model. The effect of
strong impurity scattering is analyzed and it is found to affect the ratio of
the non-diagonal (Hall) and diagonal components of the conductivity as well as
the relative importance of different mechanisms.Comment: Invited paper for Ann. Physik commemorating Paul Drud
From Primordial Quantum Fluctuations to the Anisotropies of the Cosmic
  Microwave Background Radiation

These lecture notes cover mainly three connected topics. In the first part we
give a detailed treatment of cosmological perturbation theory. The second part
is devoted to cosmological inflation and the generation of primordial
fluctuations. In part three it will be shown how these initial perturbation
evolve and produce the temperature anisotropies of the cosmic microwave
background radiation. Comparing the theoretical prediction for the angular
power spectrum with the increasingly accurate observations provides important
cosmological information (cosmological parameters, initial conditions).Comment: 203 pages, 15 figures, Based on lectures given at the
  \textit{Physik-Combo}, in Halle, Leipzig and Jena, winter semester 2004/5. To
  appear in \emph{Ann. Phys. (Leipzig
The Einstein-Cartan-Elko system

The present paper analyses the Einstein-Cartan theory of gravitation with
Elko spinors as sources of curvature and torsion. After minimally coupling the
Elko spinors to torsion, the spin angular momentum tensor is derived and its
structure is discussed. It shows a much richer structure than the Dirac
analogue and hence it is demonstrated that spin one half particles do not
necessarily yield only an axial vector torsion component. Moreover, it is
argued that the presence of Elko spinors partially solves the problem of
minimally coupling Maxwell fields to Einstein-Cartan theory.Comment: 12 pages, no figure
Equations of motion for a (non-linear) scalar field model as derived
  from the field equations

The problem of derivation of the equations of motion from the field equations
is considered. Einstein's field equations have a specific analytical form: They
are linear in the second order derivatives and quadratic in the first order
derivatives of the field variables. We utilize this particular form and propose
a novel algorithm for thederivation of the equations of motion from the field
equations. It is based on the condition of the balance between the singular
terms of the field equation. We apply the algorithm to a nonlinear Lorentz
invariant scalar field model. We show that it results in the Newton law of
attraction between the singularities of the field moved on approximately
geodesic curves. The algorithm is applicable to the $N$-body problem of the
Lorentz invariant field equations.Comment: Accepted in Annalen der Physi