What is a Quantum Integrable System?

Lecture Synopsis

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.

Biography

Alessandro Torrielli graduated in Physics from the University of Genova (Italy) in 1999, and took his PhD in Physics from the University of Padova (Italy) in 2003. He then held postdoctoral positions at Padova, the Humboldt University of Berlin (Germany), the Massachusetts Institute of Technology (MIT, USA), the University of Utrecht (the Netherlands), the University of York (United Kingdom). Since 2011 he is permanent member of staff at the University of Surrey (United Kingdom) in the Department of Mathematics, School of Mathematics and Physics.

His research interests focus on quantum integrable systems, in particularly those appearing in the context of the AdS/CFT correspondence in string theory. His research papers - with his collaborators and solo - have gathered over 3500 citations, and he has written and co-authored several well-cited reviews. In 2019 was awarded a major EPSRC-SFI research grant in cooperation with Dr Marius de Leeuw at Trinity College Dublin (Ireland).