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Conference on "Variational and spectral methods in Quantum Field Theory"
Organizers: Volker Bach (Braunschweig), Maria J. Esteban (CNRS), Mathieu Lewin (CNRS), Eric Séré (Paris-Dauphine)


Edwin Langmann (Stockholm, Sweden): "Construction by Bosonization"
Tuesday 23 April 2013, 14:00 - 14:45
Amphi Hermite


In the first part of my talk I review a construction of the massless Thirring model using a collection of mathematical results known as bosonization. I also try to put this into a historic perspective by comparing with the discussion of the massless Thirring model in influential lecture notes by Wightman from the 1960's [W].  In particular, I discuss issues like Haag's theorem, ultra-violet catastrophe, instability of vacuum from today's perspective.

In the second part of my talk I try to explain the view that the massless Thirring model is a prototype and simplest example in a class of quantum field theory models which can be constructed, and even solved exactly, by bosonization. This class of models provide a tool kid for effective descriptions of condensed matter systems with correlated fermions not only in 1+1- but also higher dimensions; they are, in general, not relativistically invariant. I mention recent results, on-going projects, and open questions.

[W] A.S. Wightman, "Introduction to Some Aspects of the Relativistic Dynamics of Quantized Fields", Cargese Lectures in Theoretical Physics, M. Levi (Ed), Gordon and Breach (1967)