837 research outputs found
Form factors and action of U_{\sqrt{-1}}(sl_2~) on infinite-cycles
Let be a sequence of
skew-symmetric polynomials in satisfying , whose coefficients are symmetric Laurent polynomials in . We
call an -cycle if
holds for all .
These objects arise in integral representations for form factors of massive
integrable field theory, i.e., the SU(2)-invariant Thirring model and the
sine-Gordon model. The variables are the integration
variables and are the rapidity variables. To each
-cycle there corresponds a form factor of the above models.
Conjecturally all form-factors are obtained from the -cycles.
In this paper, we define an action of
on the space of -cycles.
There are two sectors of -cycles depending on whether is even or
odd. Using this action, we show that the character of the space of even (resp.
odd) -cycles which are polynomials in is equal to the
level irreducible character of with lowest
weight (resp. ). We also suggest a possible tensor
product structure of the full space of -cycles.Comment: 27 pages, abstract and section 3.1 revise
Algebraic representation of correlation functions in integrable spin chains
Taking the XXZ chain as the main example, we give a review of an algebraic
representation of correlation functions in integrable spin chains obtained
recently. We rewrite the previous formulas in a form which works equally well
for the physically interesting homogeneous chains. We discuss also the case of
quantum group invariant operators and generalization to the XYZ chain.Comment: 31 pages, no figur
A recursion formula for the correlation functions of an inhomogeneous XXX model
A new recursion formula is presented for the correlation functions of the
integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators
involving n consecutive lattice sites to those with n-1 and n-2 sites. In a
series of papers by V. Korepin and two of the present authors, it was
discovered that the correlators have a certain specific structure as functions
of the inhomogeneity parameters. Our formula allows for a direct proof of this
structure, as well as an exact description of the rational functions which has
been left undetermined in the previous works.Comment: 37 pages, 1 figure, Proof of Lemma 4.8 modifie
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