11/12/2013, 17:00 — 18:00 — Room P4.35, Mathematics Building
Carlos Guedes, AEI, Golm-Potsdam
The non-commutative Fourier transform for Lie groups
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. In quantum mechanics on the Euclidean space, the standard Fourier transform gives a unitary map between the position representation -- functions on the configuration space -- and the momentum representation -- functions on the corresponding cotangent space. That is no longer the case for systems whose configuration space is a more general Lie group. In this talk I will introduce a notion of Fourier transform that extends this duality to arbitrary Lie groups.