Topological Quantum Field Theory Seminar   RSS

05/06/2007, 11:00 — 12:00 — Amphitheatre Pa3, Mathematics Building
, Institut des Hautes Études Scientifiques

New methods in renormalization theories - I

The first occurence of the ideas of renormalisation in physics is due to Green, around 1850, who used such methods to study the motion of a pendulum in a fluid. The same kind of methods was proposed by J. Oppenheimer around 1930, to take in account the so-called radiative corrections to the spectral lines of atoms. Like the previous attempts in classical electrodynamics, this approach led to unphysical infinite quantities. As it si well-known, the new methods of Bethe, Schwinger, Tomonaga, Feynman and Dyson solved in principle the problem of infinities around 1950. But a conceptual breakthrough occured ten years ago when A. Connes and D. Kreimer introduced Hopf algebraic methods in this game. We propose to explain our own verion of these methods, emphasizing a certain infinite-dimensional group, the so-called dressing group. A striking feature is the deep analogy with groups introduced by Grothendieck under the name of motivic Galois groups. These lectures shall begin with a short historical review, followed by a description of the standard calculations, and then we shall describe in detail the new methods.

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Current organizers: José MourãoRoger Picken, Marko Stošić


FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.