Quantum field theory provides an extremely accurate description of reality, but also an extremely complex one, which often can only be approached via perturbation theory and approximations. At the cost of a drastic simplification, we can study instead an integrable quantum field theory in 1+1 dimensions. In this case, the spectrum can sometimes be determined exactly, and one can derive an exact S-matrix for the scattering of particles on a line and their bound states. I will present one of the most famous integrable quantum field theories - the Lieb-Liniger model, a.k.a. non-linear Schroedinger equation. I will show how to diagonalise the quantum Hamiltonian exactly via the so-called Bethe ansatz, and how this will reveal a startling fact which could have never been seen in perturbation theory: interacting bosons which behave like fermions.
Lecturer: Professor Alessandro Torrelli
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27 авг 2024
