15th Colloquium on Mathematics and Foundations of Quantum Theory, July 14 2022

About

This event is organized alternately each seminar by the groups of Dirk - André Deckert (LMU), Wojciech Dybalski (U Poznań), Felix Finster (U Regensburg), and Peter Pickl (U Tübingen).

The event will take place on Zoom: Join us on Zoom

Program

Talks

Azam Jahandideh: Stochastic Quantization of two-dimensional Φ⁴ Euclidian Quantum Field Theory

Abstract: We revisit the construction of the measure of the Φ⁴ model of Euclidean quantum field theory in dimension two. We use the technique of stochastic quantization together with the energy technique from PDE theory. We construct the measure in infinite volume and prove that it is translationally invariant and reflection positive. One of the interesting features of our construction is the use of a non-standard UV cutoff in momentum space which preserves reflection positivity. This shows that, contrary to folk wisdom, lattice approximation is not necessary to prove reflection positivity of interacting QFT measures. Work in progress

Umut Özcan: Effective Dynamics Of A Dense Fermi Gas

Abstract: The dynamic of N fermionic particles in the one-dimensional box at zero temperature is considered. The particles are spinless and interact via a two body potential which is assumed to have a bounded and compactly supported Fourier transform. We study the time evolution of the initial state given by the Fermi sea, the ground state of non-interacting Fermi gas. More precisely we compare it with a non-interacting wave function, which differs from the initial state only by the global exp(−iEt), where E is the expectation value of the Hamiltonian in the initial state. The norm of the difference between the two wave functions is shown to be bounded by an L dependent constant times (1 + t)k_F^-1 with k_F denoting the Fermi momentum. In summary, our result shows that, under the given assumptions, the one-dimensional Fermi gas in the high-density limit (i.e. for k_F >> 1) behaves effectively like a free Fermi gas.

Giuseppe De Nittis: The Magnetic Spectral Triple: Applications and Open Questions

Abstract: Since the early works by Bellissard, non-commutative geometry (NCG) has proved to be an excellent tool for the analysis of the quantum Hall effect (QHE), and more in general for the study of the topological phases of matter. The central object of the Bellissard's NCG for the QHE is a spectral triple designed to deal with tight-binding operators. In this talk we will present a new spectral triple suitable to treat continuous magnetic operators. We will show how the QHE in the continuous can be described inside this new NCG. Certain possible new applications, along with some related open questions, will be also presented.