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.
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Translated from Ukrainskii Matematicheskii Zhurna. l, Vol. 43, No. 11, pp. 1527–1537, November, 1991.
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Gavrilik, A.M. Geometry in nonlinear quantumlike models on stiefel manifolds and bifurcations of associated autonomous systems. Ukr Math J 43, 1418–1427 (1991). https://doi.org/10.1007/BF01067281
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DOI: https://doi.org/10.1007/BF01067281