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Group analysis and renormgroup symmetries. (English) Zbl 0906.22018

The authors investigate the connection between the renormalization group which originated in quantum field theory and the group analysis of differential equations. Their strategy has four steps: (i) Construct the renormalization group manifold. (ii) Calculate the symmetry group admitted by this manifold. (iii) Restrict the obtained group to the solution of the boundary value problem under consideration. (iv) Find analytical expressions for the solutions. – The authors demonstrate this strategy with a simple example.

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds
35A22 Transform methods (e.g., integral transforms) applied to PDEs
82B28 Renormalization group methods in equilibrium statistical mechanics
81T17 Renormalization group methods applied to problems in quantum field theory
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