ar X iv : h ep - t h / 95 07 08 7 v 1 1 7 Ju l 1 99 5 Algebraic aspect and construction of Lax operators in quantum integrable systems

ar X iv : s ol v - in t / 9 90 60 08 v 1 1 5 Ju n 19 99 PARACONFORMAL STRUCTURES AND INTEGRABLE SYSTEMS

We consider some natural connections which arise between right-flat (p, q) para-conformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a " Lax p-tuple " of linear differential operators, depending a spectral parameter which lives in (q − 1)-dimensional complex projective space. Generally, the differential operators contain partial derivatives ...

ar X iv : h ep - t h / 97 09 16 8 v 2 1 1 O ct 1 99 7 Zero curvature representation for classical lattice sine - Gordon equation via quantum R - matrix

Local M-operators for the classical sine-Gordon model in discrete space-time are constructed by convolution of the quantum trigonometric 4×4 R-matrix with certain vectors in its " quantum " space. Components of the vectors are identified with τ-functions of the model. This construction generalizes the known representation of M-operators in continuous time models in terms of Lax operators and cl...

ar X iv : h ep - t h / 94 08 04 1 v 1 7 A ug 1 99 4 June 1994 Current - like variables in massive and massless integrable models 1

ar X iv : h ep - t h / 97 07 23 0 v 1 2 8 Ju l 1 99 7 A Course on : “ Quantum Field

ar X iv : h ep - t h / 94 05 08 7 v 1 1 3 M ay 1 99 4 Hirota equation as an example of integrable symplectic map ∗

The hamiltonian formalism is developed for the Sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of corresponding classical finite-dimensional system is established.