18,909 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

### 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

### 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

### A new set of exact form factors

Some mistaken reasonings at the end of the paper omitted

### Cohomologies of Affine Jacobi Varieties and Integrable Systems

We study the affine ring of the affine Jacobi variety of a hyper-elliptic
curve. The matrix construction of the affine hyper-elliptic Jacobi varieties
due to Mumford is used to calculate the character of the affine ring. By
decomposing the character we make several conjectures on the cohomology groups
of the affine hyper-elliptic Jacobi varieties. In the integrable system
described by the family of these affine hyper-elliptic Jacobi varieties, the
affine ring is closely related to the algebra of functions on the phase space,
classical observables. We show that the affine ring is generated by the highest
cohomology group over the action of the invariant vector fields on the Jacobi
variety.Comment: 33 pages, no figure

### Infinite Quantum Group Symmetry of Fields in Massive 2D Quantum Field Theory

Starting from a given S-matrix of an integrable quantum field theory in $1+1$
dimensions, and knowledge of its on-shell quantum group symmetries, we describe
how to extend the symmetry to the space of fields. This is accomplished by
introducing an adjoint action of the symmetry generators on fields, and
specifying the form factors of descendents. The braiding relations of quantum
field multiplets is shown to be given by the universal \CR-matrix. We develop
in some detail the case of infinite dimensional Yangian symmetry. We show that
the quantum double of the Yangian is a Hopf algebra deformation of a level zero
Kac-Moody algebra that preserves its finite dimensional Lie subalgebra. The
fields form infinite dimensional Verma-module representations; in particular
the energy-momentum tensor and isotopic current are in the same multiplet.Comment: 29 page

### 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

### Form-factors of the sausage model obtained with bootstrap fusion from sine-Gordon theory

We continue the investigation of massive integrable models by means of the
bootstrap fusion procedure, started in our previous work on O(3) nonlinear
sigma model. Using the analogy with SU(2) Thirring model and the O(3) nonlinear
sigma model we prove a similar relation between sine-Gordon theory and a
one-parameter deformation of the O(3) sigma model, the sausage model. This
allows us to write down a free field representation for the
Zamolodchikov-Faddeev algebra of the sausage model and to construct an integral
representation for the generating functions of form-factors in this theory. We
also clear up the origin of the singularities in the bootstrap construction and
the reason for the problem with the kinematical poles.Comment: 16 pages, revtex; references added, some typos corrected. Accepted
for publication in Physical Review

### Form factors for principal chiral field model with Wess-Zumino-Novikov-Witten term

We construct the form factors of the trace of energy-momentum tensor for the
massless model described by $SU(2)$ principal chiral field model with WZNW tern
on level 1. We explain how this construction can be generalized to a class of
integrable massless models including the flow from tricritical to critical
Ising model.Comment: 9 pages, LATE

- â€¦