170 research outputs found
Improved Conformal Mapping of the Borel Plane
The conformal mapping of the Borel plane can be utilized for the analytic
continuation of the Borel transform to the entire positive real semi-axis and
is thus helpful in the resummation of divergent perturbation series in quantum
field theory. We observe that the rate of convergence can be improved by the
application of Pad\'{e} approximants to the Borel transform expressed as a
function of the conformal variable, i.e. by a combination of the analytic
continuation via conformal mapping and a subsequent numerical approximation by
rational approximants. The method is primarily useful in those cases where the
leading (but not sub-leading) large-order asymptotics of the perturbative
coefficients are known.Comment: 6 pages, LaTeX, 2 tables; certain numerical examples adde
GAA repeat expansion mutation mouse models of Friedreich ataxia exhibit oxidative stress leading to progressive neuronal and cardiac pathology
Friedreich ataxia (FRDA) is a neurodegenerative disorder caused by an unstable GAA repeat expansion mutation within intron 1 of the FXN gene. However, the origins of the GAA repeat expansion, its unstable dynamics within different cells and tissues, and its effects on frataxin expression are not yet completely understood. Therefore, we have chosen to generate representative FRDA mouse models by using the human FXN GAA repeat expansion itself as the genetically modified mutation. We have previously reported the establishment of two lines of human FXN YAC transgenic mice that contain unstable GAA repeat expansions within the appropriate genomic context. We now describe the generation of FRDA mouse models by crossbreeding of both lines of human FXN YAC transgenic mice with heterozygous Fxn knockout mice. The resultant FRDA mice that express only human-derived frataxin show comparatively reduced levels of frataxin mRNA and protein expression, decreased aconitase activity, and oxidative stress, leading to progressive neurodegenerative and cardiac pathological phenotypes. Coordination deficits are present, as measured by accelerating rotarod analysis, together with a progressive decrease in locomotor activity and increase in weight. Large vacuoles are detected within neurons of the dorsal root ganglia (DRG), predominantly within the lumbar regions in 6-month-old mice, but spreading to the cervical regions after 1 year of age. Secondary demyelination of large axons is also detected within the lumbar roots of older mice. Lipofuscin deposition is increased in both DRG neurons and cardiomyocytes, and iron deposition is detected in cardiomyocytes after 1 year of age. These mice represent the first GAA repeat expansion-based FRDA mouse models that exhibit progressive FRDA-like pathology and thus will be of use in testing potential therapeutic strategies, particularly GAA repeat-based strategies. © 2006 Elsevier Inc. All rights reserved
Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop \epsilon expansion
The critical thermodynamics of an -component field model with cubic
anisotropy relevant to the phase transitions in certain crystals with
complicated ordering is studied within the four-loop \ve expansion using the
minimal subtraction scheme. Investigation of the global structure of RG flows
for the physically significant cases M=2, N=2 and M=2, N=3 shows that the model
has an anisotropic stable fixed point with new critical exponents. The critical
dimensionality of the order parameter is proved to be equal to
, that is exactly half its counterpart in the real hypercubic
model.Comment: 9 pages, LaTeX, no figures. Published versio
Chiral Symmetry Breaking in QCD: A Variational Approach
We develop a "variational mass" expansion approach, recently introduced in
the Gross--Neveu model, to evaluate some of the order parameters of chiral
symmetry breakdown in QCD. The method relies on a reorganization of the usual
perturbation theory with the addition of an "arbitrary quark mass , whose
non-perturbative behaviour is inferred partly from renormalization group
properties, and from analytic continuation in properties. The resulting
ansatz can be optimized, and in the chiral limit we estimate the
dynamical contribution to the "constituent" masses of the light quarks
; the pion decay constant and the quark condensate .Comment: 10 pages, no figures, LaTe
On the Divergence of Perturbation Theory. Steps Towards a Convergent Series
The mechanism underlying the divergence of perturbation theory is exposed.
This is done through a detailed study of the violation of the hypothesis of the
Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum
Field Theory. That theorem governs the validity (or lack of it) of the formal
manipulations done to generate the perturbative series in the functional
integral formalism. The aspects of the perturbative series that need to be
modified to obtain a convergent series are presented. Useful tools for a
practical implementation of these modifications are developed. Some resummation
methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure
Improved perturbation theory in the vortex liquids state of type II superconductors
We develop an optimized perturbation theory for the Ginzburg - Landau
description of thermal fluctuations effects in the vortex liquids. Unlike the
high temperature expansion which is asymptotic, the optimized expansion is
convergent. Radius of convergence on the lowest Landau level is in
2D and in 3D. It allows a systematic calculation of magnetization
and specific heat contributions due to thermal fluctuations of vortices in
strongly type II superconductors to a very high precision. The results are in
good agreement with existing Monte Carlo simulations and experiments.
Limitations of various nonperturbative and phenomenological approaches are
noted. In particular we show that there is no exact intersection point of the
magnetization curves both in 2D and 3D.Comment: 24 pages, 9 figure
Critical Exponents of the N-vector model
Recently the series for two RG functions (corresponding to the anomalous
dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been
extended to next order (seven loops) by Murray and Nickel. We examine here the
influence of these additional terms on the estimates of critical exponents of
the N-vector model, using some new ideas in the context of the Borel summation
techniques. The estimates have slightly changed, but remain within errors of
the previous evaluation. Exponents like eta (related to the field anomalous
dimension), which were poorly determined in the previous evaluation of Le
Guillou--Zinn-Justin, have seen their apparent errors significantly decrease.
More importantly, perhaps, summation errors are better determined. The change
in exponents affects the recently determined ratios of amplitudes and we report
the corresponding new values. Finally, because an error has been discovered in
the last order of the published epsilon=4-d expansions (order epsilon^5), we
have also reanalyzed the determination of exponents from the epsilon-expansion.
The conclusion is that the general agreement between epsilon-expansion and 3D
series has improved with respect to Le Guillou--Zinn-Justin.Comment: TeX Files, 27 pages +2 figures; Some values are changed; references
update
Solvable simulation of a double-well problem in PT symmetric quantum mechanics
Within quantum mechanics which works with parity-pseudo-Hermitian
Hamiltonians we study the tunneling in a symmetric double well formed by two
delta functions with complex conjugate strengths. The model is exactly solvable
and exhibits several interesting features. Besides an amazingly robust absence
of any PT symmetry breaking, we observe a quasi-degeneracy of the levels which
occurs all over the energy range including the high-energy domain. This pattern
is interpreted as a manifestation of certain "quantum beats".Comment: 12 pages incl. 7 figure
Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory
We show that in applications of variational theory to quantum field theory it
is essential to account for the correct Wegner exponent omega governing the
approach to the strong-coupling, or scaling limit. Otherwise the procedure
either does not converge at all or to the wrong limit. This invalidates all
papers applying the so-called delta-expansion to quantum field theory.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/34
Critical behavior of certain antiferromagnets with complicated ordering: Four-loop \ve-expansion analysis
The critical behavior of a complex N-component order parameter
Ginzburg-Landau model with isotropic and cubic interactions describing
antiferromagnetic and structural phase transitions in certain crystals with
complicated ordering is studied in the framework of the four-loop
renormalization group (RG) approach in (4-\ve) dimensions. By using
dimensional regularization and the minimal subtraction scheme, the perturbative
expansions for RG functions are deduced and resummed by the Borel-Leroy
transformation combined with a conformal mapping. Investigation of the global
structure of RG flows for the physically significant cases N=2 and N=3 shows
that the model has an anisotropic stable fixed point governing the continuous
phase transitions with new critical exponents. This is supported by the
estimate of the critical dimensionality obtained from six loops
via the exact relation established for the complex and real
hypercubic models.Comment: LaTeX, 16 pages, no figures. Expands on cond-mat/0109338 and includes
detailed formula
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