Extension of the Conley--Zehnder Index and Calculation of the Maslov-Type Index Intervening in Gutzwiller's Trace Formula

2005/08/25 by Maurice De Gosson, De Gosson, Maurice, Serge De Gosson +1
Mathematics · Physics and Astronomy · #37J05 #53D12 #53Z05 #81S30 #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:37J05 #msc:53D12 #msc:53Z05 #msc:81S30 #nlin.CD

paper · pdf · doi:10.48550/arxiv.math-ph/0508051

arxiv created 2005/08/26 · arxiv updated 2009/12/01

Abstract

The aim of this paper is to give an explicit formula for the calculation of the Gutzwiller--Maslov index of a Hamiltonian periodic orbit. We identify the index appearing in Gutzwiller's trace formula with a non-trivial extension of the Conley--Zehnder index. This index can be related to the usual Maslov index using the theory of the metaplectic group and the formalism of the Arnol'd--Leray--Maslov index developed in previous work, and is extended to symplectic paths with arbitrary endpoint.

Related

• Gutzwiller's Semiclassical Trace Formula and Maslov-Type Index Theory for Symplectic Paths
• Maslov indices for periodic orbits
• Maslov index of Hamiltonian systems
• On the Maslov-type index for general paths of symplectic matrices
• On a product formula for the Conley--Zehnder index of symplectic paths and its applications