On a quasimorphism of Hamiltonian diffeomorphisms and quantization

2019/10/11 by Charles, Laurent
#53D50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1910.05073

Abstract

In the setting of geometric quantization, we associate to any prequantum bundle automorphism a unitary map of the corresponding quantum space. These maps are controlled in the semiclassical limit by two invariants of symplectic topology: the Calabi morphism and a quasimorphism of the universal cover of the Hamiltonian diffeomorphism group introduced by Entov, Py, Shelukhin.

Related

• Calabi quasimorphism and quantum homology
• Asymptotic representations of Hamiltonian diffeomorphisms and quantization
• Calabi quasimorphisms for monotone coadjoint orbits
• π₁ of symplectic automorphism groups and invertibles in quantum homology rings
• Shifted geometric quantization