Geometry in nonlinear quantumlike models on stiefel manifolds and bifurcations of associated autonomous systems

Abstract

Based on the geometric characteristics of Stiefel manifolds VN,k=SO(N)/SO(N-k) that have been previously found, two-loop β functions (a matrix β function, and a pair of scalar functions) of the renormalized group and a dynamic system that together describe the renormalization group evolution of effective interaction in nonlinear σ-models on such manifolds are obtained. It is shown that for definite values of the parameter bifurcations of saddle-node type equilibrium positions are observed in this dynamic system.