Local quantum physics of systems with infinitely many interacting degrees of freedom leads to situations whose understanding often requires new physical intuition and mathematical concepts beyond that acquired in quantum mechanics and perturbative constructions in quantum field theory. In this situation twodimensional soluble models turned out to play an important role. On the one hand they ill...

The goal of this paper is to present rigorous mathematical formulations and results for Lorentzian models, introduced in physical papers. Lorentzian models represent two dimensional models, where instead of a two-dimensional lattice one considers an ensemble of triangulations of a cylinder, and natural probability measure (Gibbs family) on this ensemble. It appears that correlation functions of...

From Hamilton’s principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity connecting equations of momentum, mass, energy and entropy is obtained by extending the Gibbs identity in dynamics. The obtained system is hyperbolic for sma...