RENORMALIZATION GROUP SYMMETRY AND SOPHUS LIE GROUP ANALYSIS

Renormalization group flows and continual Lie algebras

We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebr...

Lie-Group Approach to Perturbative Renormalization-Group Method

The Lie-group approach to the perturbative renormalization group (RG) method is developed to obtain an asymptotic solutions of both autonomous and non-autonomous ordinary differential equations. Reduction of some partial differetial equations to typical RG equations is also achieved by this approach and a simple recipe for providing RG equations is presented.

Renormalization Group Renormalization Group

Time-Dependent Real-Space Renormalization Group Method

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...

Renormalization group analysis of turbulence

1. Objective The objective is to understand and extend a recent theory of turbulence based on dynamic renormalization group (RNG) techniques. The application of RNG methods to hydrodynamic turbulence has been explored most extensively by Yakhot and Orszag (1986). They calculate an eddy viscosity consistent with the Kolmogorov inertial range by systematic elimination of the small scales in the f...