Classical and quantum three-dimensional lattice field theories
Meeting Room 3, CMS
We will discuss field-theoretical aspects of q-oscillator/discrete three-wave equations. The classical limit of quantum q-oscillator model is a completely integrable Hamiltonian (Euler-Lagrange-…) system. Physical regimes of classical theories are defined by reality regimes of their lattice action/energy. The real regimes can be classified as three distinct field theories with cone-type dispersion relations and one "classical" statistical mechanics. A principal difference between statistical mechanics and field theory is that in the first case a ground state provides an absolute minimum of energy functional while in the field-theoretical cases there is a class of soliton solutions of equations of motion. Dispersion relations are related to the field-theoretical solitons. We also discuss roughly the quantum field/statistical mechanics theories corresponding to these regimes.