Fractional derivative of inverse matrix and its applications to soliton theory

In this paper, a formula of the local fractional partial derivative of inverse matrix is presented and proved. With the help of the derived formula, two new non-linear PDE are derived including the local fractional non-isospectral self-dual Yang-Mills equation and the local fractional principal chiral field equation. It is shown that the formula of the local fractional partial derivative of inverse matrix can be used to derive some other local fractional non-linear PDE in soliton theory.

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 term 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. From F. Smirnov. During several months I worked with Pierre Mejean. After his premature decease which deeply affected everybody who knew him I decided to collect and to publish the results which we obtained together.

COLLECTIVE FIELD APPROACH TO GAUGED PRINCIPAL CHIRAL FIELD AT LARGE-N

The lattice model of principal chiral field interacting with the gauge fields, which have no kinetic term, is considered. This model can be regarded as a strong coupling limit of lattice gauge theory at finite temperature. The complete set of equations for collective field variables is derived in the large-N limit and the phase structure of the model is studied.

A NEW SET OF EXACT FORM FACTORS

We present form factors for a wide range of integrable models which include marginal perturbations of the SU(2) WZNZ model for arbitrary central charge and the principal chiral field model. The interesting structure of these form factors is discussed.