14,761 research outputs found
On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
One of the two existing strategies of resolving singularities of multifold
Mellin-Barnes integrals in the dimensional regularization parameter, or a
parameter of the analytic regularization, is formulated in a modified form. The
corresponding algorithm is implemented as a Mathematica code MBresolve.mComment: LaTeX, 10 page
Asymptotic Bound-state Model for Feshbach Resonances
We present an Asymptotic Bound-state Model which can be used to accurately
describe all Feshbach resonance positions and widths in a two-body system. With
this model we determine the coupled bound states of a particular two-body
system. The model is based on analytic properties of the two-body Hamiltonian,
and on asymptotic properties of uncoupled bound states in the interaction
potentials. In its most simple version, the only necessary parameters are the
least bound state energies and actual potentials are not used. The complexity
of the model can be stepwise increased by introducing threshold effects,
multiple vibrational levels and additional potential parameters. The model is
extensively tested on the 6Li-40K system and additional calculations on the
40K-87Rb system are presented.Comment: 13 pages, 8 figure
Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams
It is shown how strictly four-dimensional integration by parts combined with
differential renormalization and its infrared analogue can be applied for
calculation of Feynman diagrams.Comment: 6 pages, late
Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
The problem of the invariant classification of the orthogonal coordinate webs
defined in Euclidean space is solved within the framework of Felix Klein's
Erlangen Program. The results are applied to the problem of integrability of
the Calogero-Moser model
Using baseline-dependent window functions for data compression and field-of-interest shaping in radio interferometry
In radio interferometry, observed visibilities are intrinsically sampled at
some interval in time and frequency. Modern interferometers are capable of
producing data at very high time and frequency resolution; practical limits on
storage and computation costs require that some form of data compression be
imposed. The traditional form of compression is a simple averaging of the
visibilities over coarser time and frequency bins. This has an undesired side
effect: the resulting averaged visibilities "decorrelate", and do so
differently depending on the baseline length and averaging interval. This
translates into a non-trivial signature in the image domain known as
"smearing", which manifests itself as an attenuation in amplitude towards
off-centre sources. With the increasing fields of view and/or longer baselines
employed in modern and future instruments, the trade-off between data rate and
smearing becomes increasingly unfavourable. In this work we investigate
alternative approaches to low-loss data compression. We show that averaging of
the visibility data can be treated as a form of convolution by a boxcar-like
window function, and that by employing alternative baseline-dependent window
functions a more optimal interferometer smearing response may be induced. In
particular, we show improved amplitude response over a chosen field of
interest, and better attenuation of sources outside the field of interest. The
main cost of this technique is a reduction in nominal sensitivity; we
investigate the smearing vs. sensitivity trade-off, and show that in certain
regimes a favourable compromise can be achieved. We show the application of
this technique to simulated data from the Karl G. Jansky Very Large Array (VLA)
and the European Very-long-baseline interferometry Network (EVN)
Magic identities for conformal four-point integrals
We propose an iterative procedure for constructing classes of off-shell
four-point conformal integrals which are identical. The proof of the identity
is based on the conformal properties of a subintegral common for the whole
class. The simplest example are the so-called `triple scalar box' and `tennis
court' integrals. In this case we also give an independent proof using the
method of Mellin--Barnes representation which can be applied in a similar way
for general off-shell Feynman integrals.Comment: 13 pages, 12 figures. New proof included with neater discussion of
contact terms. Typo correcte
Computing the Loewner driving process of random curves in the half plane
We simulate several models of random curves in the half plane and numerically
compute their stochastic driving process (as given by the Loewner equation).
Our models include models whose scaling limit is the Schramm-Loewner evolution
(SLE) and models for which it is not. We study several tests of whether the
driving process is Brownian motion. We find that just testing the normality of
the process at a fixed time is not effective at determining if the process is
Brownian motion. Tests that involve the independence of the increments of
Brownian motion are much more effective. We also study the zipper algorithm for
numerically computing the driving function of a simple curve. We give an
implementation of this algorithm which runs in a time O(N^1.35) rather than the
usual O(N^2), where N is the number of points on the curve.Comment: 20 pages, 4 figures. Changes to second version: added new paragraph
to conclusion section; improved figures cosmeticall
Numerical evaluation of multi-loop integrals by sector decomposition
In a recent paper we have presented an automated subtraction method for
divergent multi-loop/leg integrals in dimensional regularisation which allows
for their numerical evaluation, and applied it to diagrams with massless
internal lines. Here we show how to extend this algorithm to Feynman diagrams
with massive propagators and arbitrary propagator powers. As applications, we
present numerical results for the master 2-loop 4-point topologies with massive
internal lines occurring in Bhabha scattering at two loops, and for the master
integrals of planar and non-planar massless double box graphs with two
off-shell legs. We also evaluate numerically some two-point functions up to 5
loops relevant for beta-function calculations, and a 3-loop 4-point function,
the massless on-shell planar triple box. Whereas the 4-point functions are
evaluated in non-physical kinematic regions, the results for the propagator
functions are valid for arbitrary kinematics.Comment: 15 pages latex, 11 eps figures include
Form factors of descendant operators: Free field construction and reflection relations
The free field representation for form factors in the sinh-Gordon model and
the sine-Gordon model in the breather sector is modified to describe the form
factors of descendant operators, which are obtained from the exponential ones,
\e^{\i\alpha\phi}, by means of the action of the Heisenberg algebra
associated to the field . As a check of the validity of the
construction we count the numbers of operators defined by the form factors at
each level in each chiral sector. Another check is related to the so called
reflection relations, which identify in the breather sector the descendants of
the exponential fields \e^{\i\alpha\phi} and \e^{\i(2\alpha_0-\alpha)\phi}
for generic values of . We prove the operators defined by the obtained
families of form factors to satisfy such reflection relations. A generalization
of the construction for form factors to the kink sector is also proposed.Comment: 29 pages; v2: minor corrections, some references added; v3: minor
corrections; v4,v5: misprints corrected; v6: minor mistake correcte
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