Reduction, the trace formula, and semiclassical asymptotics
AUTOR(ES)
Guillemin, Victor
RESUMO
We state a theorem that relates the theory of dimensional reduction in Hamiltonian mechanics to the spectral properties of elliptic operators with symmetries on compact manifolds. As an application, we show that the spectrum of the Schrödinger operator, -[unk]hΔ + V, as [unk]h → 0, contains geometric information about the closed trajectories of a classical particle with Hamiltonian ǁpǁ2 + V(q). More generally, we show that this is true for particles with internal degrees of freedom and subject to an external Yang-Mills field, the classical limit being the Wong-Sternberg-Weinstein system for such particles.
ACESSO AO ARTIGO
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=299394Documentos Relacionados
- The Weyl character formula, the half-spin representations, and equal rank subgroups
- Cutaneous infection by Mycobacterium lentiflavum after subcutaneous injection of lipolytic formula,
- New method for obtaining complex roots in the semiclassical coherent-state propagator formula
- Denitrification, Nitrate Reduction, and Oxygen Consumption in Coastal and Estuarine Sediments
- Denitrification, Acetylene Reduction, and Methane Metabolism in Lake Sediment Exposed to Acetylene