152 research outputs found
A differential identity for Green functions
If P is a differential operator with constant coefficients, an identity is
derived to calculate the action of exp(P) on the product of two functions. In
many-body theory, P describes the interaction Hamiltonian and the identity
yields a hierarchy of Green functions. The identity is first derived for scalar
fields and the standard hierarchy is recovered. Then the case of fermions is
considered and the identity is used to calculate the generating function for
the Green functions of an electron system in a time-dependent external
potential.Comment: 14 page
The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization
Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf
algebra of renormalization in perturbative quantum field theory, we investigate
the relation between the twisted antipode axiom in that formalism, the Birkhoff
algebraic decomposition and the universal formula of Kontsevich for quantum
deformation.Comment: 21 pages, 15 figure
The structure of Green functions in quantum field theory with a general state
In quantum field theory, the Green function is usually calculated as the
expectation value of the time-ordered product of fields over the vacuum. In
some cases, especially in degenerate systems, expectation values over general
states are required. The corresponding Green functions are essentially more
complex than in the vacuum, because they cannot be written in terms of standard
Feynman diagrams. Here, a method is proposed to determine the structure of
these Green functions and to derive nonperturbative equations for them. The
main idea is to transform the cumulants describing correlations into
interaction terms.Comment: 13 pages, 6 figure
Relating on-shell and off-shell formalism in perturbative quantum field theory
In the on-shell formalism (mostly used in perturbative quantum field theory)
the entries of the time ordered product T are on-shell fields (i.e. the basic
fields satisfy the free field equations). With that, (multi)linearity of T is
incompatible with the Action Ward identity. This can be circumvented by using
the off-shell formalism in which the entries of T are off-shell fields. To
relate on- and off-shell formalism correctly, a map sigma from on-shell fields
to off-shell fields was introduced axiomatically by Duetsch and Fredenhagen. In
that paper it was shown that, in the case of one real scalar field in N=4
dimensional Minkowski space, these axioms have a unique solution. However, this
solution was given there only recursively. We solve this recurrence relation
and give a fully explicit expression for sigma in the cases of the scalar,
Dirac and gauge fields for arbitrary values of the dimension N.Comment: The case of gauge fields was added. 16 page
STATISTICAL ISSUES IN THE ANALYSIS OF MICROBIAL COMMUNITIES IN SOIL
Corn and soybean production dominates the agricultural systems of the mid-western United States. Studies have found that when a single crop species is grown continually, without the rotation of other crops, yield decline occurs. At present, this phenomenon, remains poorly understood, but there are possible links to microbial community dynamics in the associated rhizosphere soil. In this study, corn plants were grown in disturbed and undisturbed soils with a 24 year history of growth as a mono culture crop or two crops grown in annual rotation. Characteristic profiles of the microbial communities were obtained by denaturing gradient gel electrophoresis of polymerase chain reaction amplified 16S rDNA from soil extracted DNA. This problem is approached as the statistical analysis of high-dimensional multivariate binary data with an emphasis on modeling and variable selection
K-edge X-ray absorption spectra in transition metal oxides beyond the single particle approximation: shake-up many body effects
The near edge structure (XANES) in K-edge X-ray absorption spectroscopy (XAS)
is a widely used tool for studying electronic and local structure in materials.
The precise interpretation of these spectra with the help of calculations is
hence of prime importance, especially for the study of correlated materials
which have a complicated electronic structure per se. The single particle
approach, for example, has generally limited itself to the dominant dipolar
cross-section. It has long been known however that effects beyond this approach
should be taken into account, both due to the inadequacy of such calculations
when compared to experiment and the presence of shake-up many-body satellites
in core-level photoemission spectra of correlated materials. This effect should
manifest itself in XANES spectra and the question is firstly how to account for
it theoretically and secondly how to verify it experimentally. By using
state-of-the-art first principles electronic structure calculations and 1s
photoemission measurements we demonstrate that shake-up many-body effects are
present in K-edge XAS dipolar spectra of NiO, CoO and CuO at all energy scales.
We show that shake-up effects can be included in K-edge XAS spectra in a simple
way by convoluting the single-particle first-principles calculations including
core-hole effects with the 1s photoemission spectra. We thus describe all
features appearing in the XAS dipolar cross-section of NiO and CoO and obtain a
dramatic improvement with respect to the single-particle calculation in CuO.
These materials being prototype correlated magnetic oxides, our work points to
the presence of shake-up effects in K-edge XANES of most correlated transition
metal compounds and shows how to account for them, paving the way to a precise
understanding of their electronic structure.Comment: 6 pages, 4 picture
Assessing temperature effects on multipole contributions and angular dependence in core-level spectroscopies
This study aims at assessing the thermal nuclei motion effects on the multipole transition channels involved in two core-level spectroscopies, x-ray absorption spectroscopy (XAS) and x-ray Raman scattering (XRS). Temperature effects on the 1s -> s monopole, 1s -> p dipole, and 1s -> d quadrupole transitions are investigated using two reference systems for which we present original experimental data: alpha-Al2O3 at the Al K edge probed by XRS at room temperature and rutile TiO2 at the Ti K pre-edge probed by XAS at temperatures ranging from 6 to 700 K. Through the latter, this work enlightens the part of the pre-edge peak enhancement due to temperature in the K pre-edge region of 3d transition metal, which is known to be routinely used to determine the concentration, valence or symmetry of the probed element in a given sample. Nuclear thermal fluctuations are taken into account using a method based on density functional theory that consists in averaging spectra over atomic configurations, generated within the harmonic approximation and obeying quantum statistics at finite temperature. Since only a finite number of such configurations are used, the numerically averaged spectra generally lose the symmetry of the equilibrium crystal positions. In this paper, we demonstrate that the physical average has to be symmetric and propose a method to restore the physical angular dependence of the spectra. The approach is successfully applied to investigate the angular dependent XAS spectra in rutile as a function of temperature. The two systems under study allow to draw general conclusions regarding the effect of nuclear quantum fluctuations on the different transition channels available to both core-level spectroscopies.Peer reviewe
Rare earth contributions to the X-ray magnetic circular dichroism at the Co K edge in rare earth-cobalt compounds investigated by multiple-scattering calculations
The X-ray magnetic circular dichroism (XMCD) has been measured at the Co K
edge in Co-hcp and R-Co compounds (R=La, Tb, Dy). The structure of the
experimental XMCD spectra in the near-edge region has been observed to be
highly sensitive to the magnetic environment of the absorbing site.
Calculations of the XMCD have been carried out at the Co K edge in Co metal,
LaCo and TbCo within the multiple-scattering framework including the
spin-orbit coupling. In the three systems, the XMCD spectra in the near-edge
region are well reproduced. The possibility to separate and quantitatively
estimate the local effects from those due to the neighboring atoms in the XMCD
cross section makes possible a more physical understanding of the spectra. The
present results emphasize the major role played by the states of the Tb
ions in the XMCD spectrum at the Co K edge in the TbCo compound.Comment: 34 pages, revtex, 10 eps figures included with epsf, after referee
revie
On some aspects of the definition of scattering states in quantum field theory
The problem of extending quantum-mechanical formal scattering theory to a
more general class of models that also includes quantum field theories is
discussed, with the aim of clarifying certain aspects of the definition of
scattering states. As the strong limit is not suitable for the definition of
scattering states in quantum field theory, some other limiting procedure is
needed. Two possibilities are considered, the abelian limit and adiabatic
switching. Formulas for the scattering states based on both methods are
discussed, and it is found that generally there are significant differences
between the two approaches. As an illustration of the application and the
features of these formulas, S-matrix elements and energy corrections in two
quantum field theoretical models are calculated using (generalized)
old-fashioned perturbation theory. The two methods are found to give equivalent
results.Comment: 20 page
A smooth introduction to the wavefront set
The wavefront set provides a precise description of the singularities of a
distribution. Because of its ability to control the product of distributions,
the wavefront set was a key element of recent progress in renormalized quantum
field theory in curved spacetime, quantum gravity, the discussion of time
machines or quantum energy inequalitites. However, the wavefront set is a
somewhat subtle concept whose standard definition is not easy to grasp. This
paper is a step by step introduction to the wavefront set, with examples and
motivation. Many different definitions and new interpretations of the wavefront
set are presented. Some of them involve a Radon transform.Comment: 29 pages, 7 figure
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