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
نویسنده
چکیده
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 classical r-matrix.
منابع مشابه
/ 97 09 16 8 v 1 2 3 Se p 19 97 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...
متن کاملar 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.
متن کاملar X iv : h ep - t h / 93 10 11 7 v 1 1 9 O ct 1 99 3 QUANTUM κ - POINCARE IN ANY DIMENSION
The κ-deformation of the D-dimensional Poincaré algebra (D ≥ 2) with any signature is given. Further the quadratic Poisson brackets, determined by the classical r-matrix are calculated, and the quantum Poincaré group " with noncommuting parameters " is obtained.
متن کاملar X iv : h ep - t h / 92 10 12 8 v 1 2 3 O ct 1 99 2 Classical R - matrix structure for the Calogero model
A classical R-matrix structure is described for the Lax representation of the integrable n-particle chains of Calogero-Olshanetski-Perelomov. This R-matrix is dynamical, non antisymmetric and non-invertible. It immediately triggers the integrability of the Type I, II and III potentials, and the algebraic structures associated with the Type V potential.
متن کاملar X iv : h ep - t h / 98 10 23 4 v 1 2 8 O ct 1 99 8 FUNCTIONAL APPROACH TO PHASE SPACE FORMULATION OF QUANTUM MECHANICS
We present BRST gauge fixing approach to quantum mechanics in phase space. The theory is obtained by ¯ h-deformation of the cohomological classical mechanics described by d = 1, N = 2 model. We use the extended phase space supplied by the path integral formulation with ¯ h-deformed symplectic structure.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997