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## Perturbation splitting for more accurate eigenvalues

Fonte: Society for Industrial and Applied Mathematics (SIAM)
Publicador: Society for Industrial and Applied Mathematics (SIAM)

Tipo: Artigo de Revista Científica

Publicado em /02/2009
ENG

Relevância na Pesquisa

45.98%

Let $T$ be a symmetric tridiagonal matrix with entries and
eigenvalues of different magnitudes. For some $T$, small entrywise
relative perturbations induce small errors in the eigenvalues,
independently of the size of the entries of the matrix; this is
certainly true when the perturbed matrix can be written as
$widetilde{T}=X^{T}TX$ with small $||X^{T}X-I||$. Even if it is
not possible to express in this way the perturbations in every
entry of $T$, much can be gained by doing so for as many as
possible entries of larger magnitude. We propose a technique which
consists of splitting multiplicative and additive perturbations
to produce new error bounds which, for some matrices, are much
sharper than the usual ones. Such bounds may be useful in the
development of improved software for the tridiagonal eigenvalue
problem, and we describe their role in the context of a mixed
precision bisection-like procedure. Using the very same idea of
splitting perturbations (multiplicative and additive), we show
that when $T$ defines well its eigenvalues, the numerical values
of the pivots in the usual decomposition $T-lambda I=LDL^{T}$ may
be used to compute approximations with high relative precision.; Fundação para a Ciência e Tecnologia (FCT) - POCI 2010

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## Building the full fermion-photon vertex of QED by imposing multiplicative renormalizability of the Schwinger-Dyson equations for the fermion and photon propagators

Fonte: American Physical Soc
Publicador: American Physical Soc

Tipo: Artigo de Revista Científica

Publicado em //2009
EN

Relevância na Pesquisa

35.93%

In principle, calculation of a full Green’s function in any field theory requires knowledge of the infinite set of multipoint Green’s functions, unless one can find some way of truncating the corresponding Schwinger-Dyson equations. For the fermion and boson propagators in QED this requires an ansatz for the full 3-point vertex. Here we illustrate how the properties of gauge invariance, gauge covariance and multiplicative renormalizability impose severe constraints on this fermion-boson interaction, allowing a consistent truncation of the propagator equations. We demonstrate how these conditions imply that the 3-point vertex in the propagator equations is largely determined by the behavior of the fermion propagator itself and not by knowledge of the many higher-point functions. We give an explicit form for the fermion-photon vertex, which in the fermion and photon propagator fulfills these constraints to all orders in leading logarithms for massless QED, and accords with the weak coupling limit in perturbation theory at O(α). This provides the first attempt to deduce nonperturbative Feynman rules for strong physics calculations of propagators in massless QED that ensure a more consistent truncation of the 2-point Schwinger-Dyson equations. The generalization to next-to-leading order and masses will be described in a longer publication.; Ayse Kizilersu and Michael R. Pennington

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## Multiplicative Lidskii's inequalities and optimal perturbations of frames

Fonte: Elsevier Science Inc
Publicador: Elsevier Science Inc

Tipo: info:eu-repo/semantics/article; info:ar-repo/semantics/artículo; info:eu-repo/semantics/publishedVersion
Formato: application/pdf

ENG

Relevância na Pesquisa

35.88%

#perturbation of frames#majorization#Lidskii's inequality#convex potentials#Matemática Pura#Matemáticas#CIENCIAS NATURALES Y EXACTAS

In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame F={fj}j∈In for Cd we compute those dual frames G of F that are optimal perturbations of the canonical dual frame for F under certain restrictions on the norms of the elements of G. On the other hand, we compute those V⋅F={Vfj}j∈In – for invertible operators V which are close to the identity – that are optimal perturbations of F. That is, we compute the optimal perturbations of F among frames G={gj}j∈In that have the same linear relations as F. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.; Fil: Massey, Pedro Gustavo. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina; Fil: Ruiz...

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## Accurate solution of structured least squares problems via rank-revealing decompositions

Fonte: Society for Industrial and Applied Mathematics
Publicador: Society for Industrial and Applied Mathematics

Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article

Publicado em /07/2013
ENG

Relevância na Pesquisa

66.03%

#Accurate solutions#least squares problems#multiplicative perturbation theory#rank revealing decompositions#structured matrices#Moore–Penrose pseudoinverse.#Matemáticas

Least squares problems min(x) parallel to b - Ax parallel to(2) where the matrix A is an element of C-mXn (m >= n) has some particular structure arise frequently in applications. Polynomial data fitting is a well-known instance of problems that yield highly structured matrices, but many other examples exist. Very often, structured matrices have huge condition numbers kappa(2)(A) = parallel to A parallel to(2) parallel to A(dagger)parallel to(2) (A(dagger) is the Moore-Penrose pseudoinverse of A) and therefore standard algorithms fail to compute accurate minimum 2-norm solutions of least squares problems. In this work, we introduce a framework that allows us to compute minimum 2-norm solutions of many classes of structured least squares problems accurately, i.e., with errors parallel to(x) over cap (0) - x(0)parallel to(2)/parallel to x(0)parallel to(2) = O(u), where u is the unit roundoff, independently of the magnitude of kappa(2)(A) for most vectors b. The cost of these accurate computations is O(n(2)m) flops, i.e., roughly the same cost as standard algorithms for least squares problems. The approach in this work relies in computing first an accurate rank-revealing decomposition of A, an idea that has been widely used in recent decades to compute...

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## Additive and multiplicative renormalization of topological charge with improved gluon/fermion actions: A test case for 3-loop vacuum calculations, using overlap or clover fermions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

35.88%

We calculate perturbative renormalization properties of the topological
charge, using the standard lattice discretization given by a product of twisted
plaquettes. We use the overlap and clover action for fermions, and the Symanzik
improved gluon action for 4- and 6-link loops.
We compute the multiplicative renormalization of the topological charge
density to one loop; this involves only the gluon part of the action. The power
divergent additive renormalization of the topological susceptibility is
calculated to 3 loops.
Our work serves also as a test case of the techniques and limitations of
lattice perturbation theory, it being the first 3-loop computation in the
literature involving overlap fermions.; Comment: 15 pages, 7 figures. Final version, accepted in Physical Review D

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## Improved Perturbation Theory for Improved Lattice Actions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/05/2006

Relevância na Pesquisa

46.03%

We study a systematic improvement of perturbation theory for gauge fields on
the lattice; the improvement entails resumming, to all orders in the coupling
constant, a dominant subclass of tadpole diagrams.
This method, originally proposed for the Wilson gluon action, is extended
here to encompass all possible gluon actions made of closed Wilson loops; any
fermion action can be employed as well. The effect of resummation is to replace
various parameters in the action (coupling constant, Symanzik coefficients,
clover coefficient) by ``dressed'' values; the latter are solutions to certain
coupled integral equations, which are easy to solve numerically.
Some positive features of this method are: a) It is gauge invariant, b) it
can be systematically applied to improve (to all orders) results obtained at
any given order in perturbation theory, c) it does indeed absorb in the dressed
parameters the bulk of tadpole contributions.
Two different applications are presented: The additive renormalization of
fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector
(axial) current. In many cases where non-perturbative estimates of
renormalization functions are also available for comparison, the agreement with
improved perturbative results is significantly better as compared to results
from bare perturbation theory.; Comment: 17 pages...

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## Triviality of $\phi^4_4$ theory: small volume expansion and new data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/12/2010

Relevância na Pesquisa

45.85%

#High Energy Physics - Lattice#Condensed Matter - Statistical Mechanics#High Energy Physics - Theory

We study a renormalized coupling g and mass m in four dimensional phi^4
theory on tori with finite size z=mL. Precise numerical values close to the
continuum limit are reported for z=1,2,4, based on Monte Carlo simulations
performed in the equivalent all-order strong coupling reformulation. Ordinary
renormalized perturbation theory is found to work marginally at z=2 and and to
fail at z=1. By exactly integrating over the constant field mode we set up a
renormalized expansion in z and compute three nontrivial orders. These results
reasonably agree with the numerical data at small z. In the new expansion, the
universal continuum limit exists as expected from multiplicative
renormalizability. The triviality scenario is corroborated with significant
precision.; Comment: 27 pages, 7 figures, 4 tables

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## Form factors and non-local Multiplicative Anomaly for fermions with background torsion

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/02/2014

Relevância na Pesquisa

45.93%

We analyse the Multiplicative Anomaly (MA) in the case of quantized massive
fermions coupled to a background torsion. The one-loop Effective Action (EA)
can be expressed in terms of the logarithm of determinant of the appropriate
first-order differential operator acting in the spinors space. Simple algebraic
manipulations on determinants must be used in order to apply properly the
Schwinger-DeWitt technique, or even the covariant perturbation theory
(Barvinsky and Vilkovisky, 1990), which is used in the present work. By this
method, we calculate the finite non-local quantum corrections, and analyse
explicitly the breakdown of those algebraic manipulations on determinants,
called by MA. This feature comes from the finite non-local EA, but does not
affect the results in the UV limit, in particular the beta-functions. Similar
results was also obtained in previous papers but for different external fields
(QED and scalar field).; Comment: LaTeX file, 12 pages, no figures

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## Non-Perturbative Evaluation of the Physical Classical Velocity in the Lattice Heavy Quark Effective Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/03/1997

Relevância na Pesquisa

35.83%

In the lattice formulation of the Heavy Quark Effective Theory, the value of
the classical velocity v, as defined through the separation of the 4-momentum
of a heavy quark into a part proportional to the heavy quark mass and a
residual part which remains finite in the heavy quark limit (P = Mv + p) is
different from its value as it appears in the bare heavy quark propagator (S(p)
= 1/vp). The origin of the difference, which is effectively a lattice-induced
renormalization, is the reduction of Lorentz (or O(4)) invariance to
(hyper)-cubic invariance. The renormalization is finite and depends
specifically on the form of the discretization of the reduced heavy quark Dirac
equation. For the Forward Time - Centered Space discretization, we compute this
renormalization non-perturbatively, using an ensemble of lattices at beta = 6.1
provided by the Fermilab ACP-MAPS Collaboration. The calculation makes crucial
use of a variationally optimized smeared operator for creating composite
heavy-light mesons. It has the property that its propagator achieves an
asymptotic plateau in just a few Euclidean time steps. For comparison, we also
compute the shift perturbatively, to one loop in lattice perturbation theory.
The non-perturbative calculation of the leading multiplicative shift in the
classical velocity is considerably different from the one-loop estimate...

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## On the renormalisation group for the boundary Truncated Conformal Space Approach

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/04/2011

Relevância na Pesquisa

35.9%

In this paper we continue the study of the truncated conformal space approach
to perturbed boundary conformal field theories. This approach to perturbation
theory suffers from a renormalisation of the coupling constant and a
multiplicative renormalisation of the Hamiltonian. We show how these two
effects can be predicted by both physical and mathematical arguments and prove
that they are correct to leading order for all states in the TCSA system. We
check these results using the TCSA applied to the tri-critical Ising model and
the Yang-Lee model. We also study the TCSA of an irrelevant
(non-renormalisable) perturbation and find that, while the convergence of the
coupling constant and energy scales are problematic, the renormalised and
rescaled spectrum remain a very good fit to the exact result, and we find a
numerical relationship between the IR and UV couplings describing a particular
flow. Finally we study the large coupling behaviour of TCSA and show that it
accurately encompasses several different fixed points.; Comment: 27 pages, 19 figures

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## Non-Fermi liquid theory of a compactified Anderson single-impurity model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/04/1996

Relevância na Pesquisa

36%

We consider a version of the symmetric Anderson impurity model (compactified)
which has a non-Fermi liquid weak coupling regime. We find that in the Majorana
fermion representation, perturbation theory can be conveniently developed in
terms of Pfaffian determinants and we use this formalism to calculate the
impurity free energy, self energies, and vertex functions. In the second-order
perturbation theory, a linear temperature dependence of electrical resistivity
is obtained, and the leading corrections to the impurity specific heat are
found to behave as $T\ln T$. The impurity susceptibilities have terms in $\ln
T$ to zero, first, and second order, and corrections of $\ln^2 T$ to second
order as well. The singlet superconducting paired susceptibility at the
impurity site, is found to have second-order corrections $\ln T$, which we
interpret as an indication that a singlet conduction electron pairing resonance
forms at the Fermi level. When the perturbation theory is extended to third
order logarithmic divergences are found in the vertex function
$\Gamma_{0,1,2,3}(0,0,0,0)$. Multiplicative renormalization-group method is
then used to sum all the leading order logarithmic contributions, giving rise
to a new weak-coupling low-temperature energy scale $T_c=\Delta{\rm
exp}\left[-\frac{1}{9}\left(\frac{\pi\Delta}{U} \right )^{2}\right]$. The
scaling equation shows the dimensionless coupling constant
$\frac{U}{\pi\Delta}$ is increased as the energy scale $\Delta$ reduces. Our
perturbational results can be justified only in the regime $T>T_c$.; Comment: 40 pages...

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## Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

35.93%

It is known that the gauge field and its composite operators evolved by the
Yang--Mills gradient flow are ultraviolet (UV) finite without any
multiplicative wave function renormalization. In this paper, we prove that the
gradient flow in the 2D $O(N)$ non-linear sigma model possesses a similar
property: The flowed $N$-vector field and its composite operators are UV finite
without multiplicative wave function renormalization. Our proof in all orders
of perturbation theory uses a $(2+1)$-dimensional field theoretical
representation of the gradient flow, which possesses local gauge invariance
without gauge field. As application of the UV finiteness of the gradient flow,
we construct the energy--momentum tensor in the lattice formulation of the
$O(N)$ non-linear sigma model that automatically restores the correct
normalization and the conservation law in the continuum limit.; Comment: 32 pages, 15 figures, the tittle has been changed, the final version
to appear in PTEP

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## Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/04/2009

Relevância na Pesquisa

45.96%

In principle, calculation of a full Green's function in any field theory
requires knowledge of the infinite set of multi-point Green's functions, unless
one can find some way of truncating the corresponding Schwinger-Dyson
equations. For the fermion and boson propagators in QED this requires an {\it
ansatz} for the full three point vertex. Here we illustrate how the properties
of gauge invariance, gauge covariance and multiplicative renormalizability
impose severe constraints on this fermion-boson interaction, allowing a
consistent truncation of the propagator equations. We demonstrate how these
conditions imply that the 3-point vertex {\bf in the propagator equations} is
largely determined by the behaviour of the fermion propagator itself and not by
knowledge of the many higher point functions. We give an explicit form for the
fermion-photon vertex, which in the fermion and photon propagator fulfills
these constraints to all orders in leading logarithms for massless QED, and
accords with the weak coupling limit in perturbation theory at ${\cal
O}(\alpha)$. This provides the first attempt to deduce non-perturbative Feynman
rules for strong physics calculations of propagators in massless QED that
ensures a more consistent truncation of the 2-point Schwinger-Dyson equations.
The generalisation to next-to-leading order and masses will be described in a
longer publication.; Comment: 57 pages...

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## Functional integral approach for multiplicative stochastic processes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

35.96%

We present a functional formalism to derive a generating functional for
correlation functions of a multiplicative stochastic process represented by a
Langevin equation. We deduce a path integral over a set of fermionic and
bosonic variables without performing any time discretization. The usual
prescriptions to define the Wiener integral appear in our formalism in the
definition of Green functions in the Grassman sector of the theory. We also
study non-perturbative constraints imposed by BRS symmetry and supersymmetry on
correlation functions. We show that the specific prescription to define the
stochastic process is wholly contained in tadpole diagrams. Therefore, in a
supersymmetric theory the stochastic process is uniquely defined since tadpole
contributions cancels at all order of perturbation theory.; Comment: 9 pages, no figures, appendix added, references added, final version
as will appear in PRE.

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## Improving perturbation theory with cactus diagrams

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/12/2006

Relevância na Pesquisa

46.04%

We study a systematic improvement of perturbation theory for gauge fields on
the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders
in the coupling constant, a dominant subclass of tadpole diagrams.
This method, originally proposed for the Wilson gluon action, is extended
here to encompass all possible gluon actions made of closed Wilson loops; any
fermion action can be employed as well. The effect of resummation is to replace
various parameters in the action (coupling constant, Symanzik and clover
coefficient) by ``dressed'' values; the latter are solutions to certain coupled
integral equations, which are easy to solve numerically.
Some positive features of this method are: a) It is gauge invariant, b) it
can be systematically applied to improve (to all orders) results obtained at
any given order in perturbation theory, c) it does indeed absorb in the dressed
parameters the bulk of tadpole contributions.
Two different applications are presented: The additive renormalization of
fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector
(axial) current. In many cases where non-perturbative estimates of
renormalization functions are also available for comparison, the agreement with
improved perturbative results is consistently better as compared to results
from bare perturbation theory.; Comment: 7 pages...

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## Cumulant Dynamics of a Population under Multiplicative Selection, Mutation and Drift

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

36.06%

We revisit the classical population genetics model of a population evolving
under multiplicative selection, mutation and drift. The number of beneficial
alleles in a multi-locus system can be considered a trait under exponential
selection. Equations of motion are derived for the cumulants of the trait
distribution in the diffusion limit and under the assumption of linkage
equilibrium. Because of the additive nature of cumulants, this reduces to the
problem of determining equations of motion for the expected allele distribution
cumulants at each locus. The cumulant equations form an infinite dimensional
linear system and in an authored appendix Adam Prugel-Bennett provides a closed
form expression for these equations. We derive approximate solutions which are
shown to describe the dynamics well for a broad range of parameters. In
particular, we introduce two approximate analytical solutions: (1) Perturbation
theory is used to solve the dynamics for weak selection and arbitrary mutation
rate. The resulting expansion for the system's eigenvalues reduces to the known
diffusion theory results for the limiting cases with either mutation or
selection absent. (2) For low mutation rates we observe a separation of
time-scales between the slowest mode and the rest which allows us to develop an
approximate analytical solution for the dominant slow mode. The solution is
consistent with the perturbation theory result and provides a good
approximation for much stronger selection intensities.; Comment: Minor changes and authored appendix by Adam Prugel-Bennett. To appear
in Theoretical Population Biology...

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## Renormalization-Group Improvement of Effective Actions Beyond Summation of Leading Logarithms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

35.85%

Invariance of the effective action under changes of the renormalization scale
$\mu$ leads to relations between those (presumably calculated) terms
independent of $\mu$ at a given order of perturbation theory and those higher
order terms dependent on logarithms of $\mu$. This relationship leads to
differential equations for a sequence of functions, the solutions of which give
closed form expressions for the sum of all leading logs, next to leading logs
and subsequent subleading logarithmic contributions to the effective action.
The renormalization group is thus shown to provide information about a model
beyond the scale dependence of the model's couplings and masses. This procedure
is illustrated using the $\phi_6^3$ model and Yang-Mills theory. In the latter
instance, it is also shown by using a modified summation procedure that the
$\mu$ dependence of the effective action resides solely in a multiplicative
factor of $g^2 (\mu)$ (the running coupling). This approach is also shown to
lead to a novel expansion for the running coupling in terms of the one-loop
coupling that does not require an order-by-order redefinition of the scale
factor $\Lambda_{QCD}$. Finally, logarithmic contributions of the instanton
size to the effective action of an SU(2) gauge theory are summed...

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## Gauge transformations in relativistic two-particle constraint theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/09/1996

Relevância na Pesquisa

45.86%

Using connection with quantum field theory, the infinitesimal covariant
abelian gauge transformation laws of relativistic two-particle constraint
theory wave functions and potentials are established and weak invariance of the
corresponding wave equations shown. Because of the three-dimensional projection
operation, these transformation laws are interaction dependent. Simplifications
occur for local potentials, which result, in each formal order of perturbation
theory, from the infra-red leading effects of multiphoton exchange diagrams. In
this case, the finite gauge transformation can explicitly be represented, with
a suitable approximation and up to a multiplicative factor, by a momentum
dependent unitary operator that acts in $x$-space as a local dilatation
operator. The latter is utilized to reconstruct from the Feynman gauge the
potentials in other linear covariant gauges. The resulting effective potential
of the final Pauli-Schr\"odinger type eigenvalue equation has the gauge
invariant attractive singularity $\alpha^2/r^2$, leading to a gauge invariant
critical coupling constant $\alpha_c =1/2$.; Comment: 32 pages, latex file with 3 figures, uses epsfile.sty for figures

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## Ultraviolet divergences and factorization for coordinate-space amplitudes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

35.83%

We consider the coordinate-space matrix elements that correspond to
fixed-angle scattering amplitudes involving partons and Wilson lines in
coordinate space, working in Feynman gauge. In coordinate space, both collinear
and short-distance limits produce ultraviolet divergences. We classify
singularities in coordinate space, and identify neighborhoods associated
unambiguously with individual subspaces (pinch surfaces) where the integrals
are singular. The set of such regions is finite for any diagram. Within each of
these regions, coordinate-space soft-collinear and hard-collinear
approximations reproduce singular behavior. Based on this classification of
regions and approximations, we develop a series of nested subtraction
approximations by analogy to the formalism in momentum space. This enables us
to rewrite each amplitude as a sum of terms to which gauge theory Ward
identities can be applied, factorizing them into hard, jet and soft factors,
and to confirm the multiplicative renormalizability of products of lightlike
Wilson lines. We study in some detail the simplest case, the color-singlet cusp
linking two Wilson lines, and show that the logarithm of this amplitude, which
is a sum of diagrams known as webs, is closely related to the corresponding
subtracted amplitude order by order in perturbation theory. This enables us to
confirm that the logarithm of the cusp can be written as the integral of an
ultraviolet-finite function over a surface. We study to what extent this result
generalizes to amplitudes involving multiple Wilson lines.; Comment: 51 pages...

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## Implications of Analyticity to Mass Gap, Color Confinement and Infrared Fixed Point in Yang--Mills theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

45.85%

Analyticity of gluon and Faddeev--Popov ghost propagators and their form
factors on the complex momentum-squared plane is exploited to continue
analytically the ultraviolet asymptotic form calculable by perturbation theory
into the infrared non-perturbative solution. We require the non-perturbative
multiplicative renormalizability to write down the renormalization group
equation. These requirements enable one to settle the value of the exponent
characterizing the infrared asymptotic solution with power behavior which was
originally predicted by Gribov and has recently been found as approximate
solutions of the coupled truncated Schwinger--Dyson equations. For this
purpose, we have obtained all the possible superconvergence relations for the
propagators and form factors in both the generalized Lorentz gauge and the
modified Maximal Abelian gauge. We show that the transverse gluon propagators
are suppressed in the infrared region to be of the massive type irrespective of
the gauge parameter, in agreement with the recent result of numerical
simulations on a lattice. However, this method alone is not sufficient to
specify some of the ghost propagators which play the crucial role in color
confinement. Combining the above result with the renormalization group equation
again...

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