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Relative Phase Shifts for Metaplectic Isotopies Acting on Gaussians

Oberseminar Analysis und Theoretische Physik, 14.11.2017


Let ρ be a positive trace class operator with Gaussian Weyl symbol and (S_{t}) a one-parameter family of metaplectic operators such that S₀ is the identity. By definition the associated Pancharatnam- Sjöqvist phase ϕ(t) is the argument of Tr(S_{t}ρ). When ρ is the rank-one orthogonal projection on a vector ψ then ϕ(t) is given by Pancharatnam's formula ϕ(t)=Arg(S_{t}ψ|ψ)_{L²}. We show that ϕ(t) can be calculated explicitly by using a generalization of the Conley--Zehnder index we have defined in previous work. This gives us the opportunity to review related notions such as the Leray index and the Maslov index for symplectic paths.

Url http://www.ifam.uni-hannover.de/os_analysis.html

Prof. Dr. Maurice de Gosson, Universität Wien


Institut für Analysis

Date 14.11.2017
15:00 o'clock - 17:00 o'clock
Location Building: 1101
Room: c311
Welfengarten 1
30167 Hannover