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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 8: Quantum Field Theory II
MP 8.2: Talk
Wednesday, March 20, 2024, 10:00–10:20, HL 001
The Bałaban variational problem in the non-linear sigma model — •Wojciech Dybalski1, Alexander Stottmeister2, and Yoh Tanimoto3 — 1AMU Poznań — 2University of Hannover — 3University of Rome ``Tor Vergata"
The minimization of the action of a QFT with a constraint dictated by the block averaging procedure is an important part of the Bałaban's approach to renormalization. It is particularly interesting for QFTs with non-trivial target spaces, such as gauge theories or non-linear sigma models on a lattice. We analyse this step for the O(4) non-linear sigma model in two dimensions and demonstrate in this case how various ingredients of the Bałaban approach play together. First, using variational calculus on Lie groups, the equation for the minimum is derived. Then this non-linear equation is solved by the Banach fixed point theorem. This step requires detailed control of the lattice Green functions and their integral kernels via random walk expansions.
Keywords: sigma model; renormalization; lattice QFT; Green functions; variational calculus