Symplectic spectral geometry of semiclassical operators

2013/03/11 by Álvaro Pelayo, Pelayo, Álvaro
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #math.SP

paper · pdf · doi:10.48550/arxiv.1303.2570

To appear in Bulletin of the Belgian Mathematical Society, 11 pages

arxiv created 2013/03/11 · arxiv updated 2013/03/12

Abstract

In the past decade there has been a flurry of activity at the intersection of spectral theory and symplectic geometry. In this paper we review recent results on semiclassical spectral theory for commuting Berezin-Toeplitz and h-pseudodifferential operators. The paper emphasizes the interplay between spectral theory of operators (quantum theory) and symplectic geometry of Hamiltonians (classical theory), with an eye towards recent developments on the geometry of finite dimensional integrable systems.

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