Quantum Weak Values and Harmonic Analysis on Lie Groups
Keywords:
Grossman-Royer, Weyl-Heisenberg, weak values, Lie groups, pre- and post-selection, Haar measure, group representation, special unitary group SU(2), special orthogonal group SO(3)Abstract
The aim of this contribution is to generalize a formula proved by Maurice de Gosson (de Gosson 2017) about weak values in the context of the phase-space formulation of Quantum Mechanics (Rundle and Everitt 2021), in order to express those weak values using tools coming from the harmonic analysis on Lie Groups (Faraut 2006). A general formula which enables us to compute weak values is proved, in which the integration on a Lie Group is substituted to the integration on phase-space, using Haar measures. Then this formula is applied to SU(2) and SO(3) and also to the quotient group G/H, where H is a normal subgroup of G.
