Noncommutative Fourier transforms and quantum mechanics on Lie groups

par Mathieu Beauvillain

vendredi 27 févr. 2026, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Bat. Braconnier)

In standard quantum mechanics the Fourier transform can be interpreted as a mapping from functions of the classical positions to functions of the classical momenta. This interpretation allows to define semiclassical quantities such as Wigner functions and path integrals. In the case of quantum mechanics on a compact Lie group, the momentum space is often understood as the set of irreducible representations through Peter-Weyl theorem. However, not being a space of functions of the classical momenta, it is not very suitable for semiclassics. I will therefore show how to construct an alternate momentum space consisting in functions of the classical momenta and define a Fourier transform relating it to the position space of square integrable functions of the group. If time permits, I will also discuss how the construction naturally leads to a generalisation of the Poisson summation formula.