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A Gutzwiller type formula for a reduced Hamiltonian within the framework of symmetry. (English. Abridged French version) Zbl 1142.81331

Summary: For a classical Hamiltonian with a finite group of symmetries, we give semi-classical asymptotics in a neighbourhood of an energy \(E\) of a regularized spectral density of the quantum Hamiltonian restricted to symmetry subspaces of Peter-Weyl defined by irreducible characters of the group. If we suppose that the energy level \(\Sigma_{E}\) is compact, non-critical, and that its periodic orbits are non-degenerate, we get a Gutzwiller type formula for the reduced Hamiltonian, whose oscillating part involves the symmetry properties of closed trajectories of \(\Sigma_{E}\).

MSC:

81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35A30 Geometric theory, characteristics, transformations in context of PDEs
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
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