27,950 research outputs found
On the deformation of abelian integrals
We consider the deformation of abelian integrals which arose from the study
of SG form factors. Besides the known properties they are shown to satisfy
Riemann bilinear identity. The deformation of intersection number of cycles on
hyperelliptic curve is introduced.Comment: 8 pages, AMSTE
Gauge-Invariant Differential Renormalization: Abelian Case
A new version of differential renormalization is presented. It is based on
pulling out certain differential operators and introducing a logarithmic
dependence into diagrams. It can be defined either in coordinate or momentum
space, the latter being more flexible for treating tadpoles and diagrams where
insertion of counterterms generates tadpoles. Within this version, gauge
invariance is automatically preserved to all orders in Abelian case. Since
differential renormalization is a strictly four-dimensional renormalization
scheme it looks preferable for application in each situation when dimensional
renormalization meets difficulties, especially, in theories with chiral and
super symmetries. The calculation of the ABJ triangle anomaly is given as an
example to demonstrate simplicity of calculations within the presented version
of differential renormalization.Comment: 15 pages, late
Geometric approach to asymptotic expansion of Feynman integrals
We present an algorithm that reveals relevant contributions in
non-threshold-type asymptotic expansion of Feynman integrals about a small
parameter. It is shown that the problem reduces to finding a convex hull of a
set of points in a multidimensional vector space.Comment: 6 pages, 2 figure
The static quark potential to three loops in perturbation theory
The static potential constitutes a fundamental quantity of Quantum
Chromodynamics. It has recently been evaluated to three-loop accuracy. In this
contribution we provide details on the calculation and present results for the
14 master integrals which contain a massless one-loop insertion.Comment: 6 pages, talk presented at Loops and Legs in Quantum Field Theory
2010, W\"orlitz, Germany, April 25-30, 201
Baxter equations and Deformation of Abelian Differentials
In this paper the proofs are given of important properties of deformed
Abelian differentials introduced earlier in connection with quantum integrable
systems. The starting point of the construction is Baxter equation. In
particular, we prove Riemann bilinear relation. Duality plays important role in
our consideration. Classical limit is considered in details.Comment: 28 pages, 1 figur
Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in
Applications of a method recently suggested by one of the authors (R.L.) are
presented. This method is based on the use of dimensional recurrence relations
and analytic properties of Feynman integrals as functions of the parameter of
dimensional regularization, . The method was used to obtain analytical
expressions for two missing constants in the -expansion of the most
complicated master integrals contributing to the three-loop massless quark and
gluon form factors and thereby present the form factors in a completely
analytic form. To illustrate its power we present, at transcendentality weight
seven, the next order of the -expansion of one of the corresponding
most complicated master integrals. As a further application, we present three
previously unknown terms of the expansion in of the three-loop
non-planar massless propagator diagram. Only multiple values at integer
points are present in our result.Comment: Talk given at the International Workshop `Loops and Legs in Quantum
Field Theory' (April 25--30, 2010, W\"orlitz, Germany)
Counting the local fields in SG theory.
In terms of the form factor bootstrap we describe all the local fields in SG
theory and check the agreement with the free fermion case. We discuss the
interesting structure responsible for counting the local fields.Comment: 16 pages AMSTEX References to the papers by A. Koubek and G. Mussargo
are added. In view of them the stasus of the problem with scalar S-matrices
is reconsidered
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