Variational Method in 1+1 Dimensional Relativistic Field Theory

by Prof. Antoine Tilloy (Mines Paris-Tech)

Wednesday Oct 27, 2021, 10:00 AM → 11:30 AM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods usually break one of the 3, which translates into the need to have an IR or UV cutoff. I will explain how a relativistic modification of continuous matrix product states allows us to satisfy the 3 requirements jointly in 1+1 dimensions. Optimizing over this class of states, one can solve scalar QFT without UV cutoff and directly in the thermodynamic limit, and numerics are promising. I will try to cover both the general philosophy of the method, the basics of the computations, and mention the many open problems.

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IHES Covid-19 regulations:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

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