Geometric quantization of Hamiltonian flows and the Gutzwiller trace formula

Autor:	Louis Ioos
Rok vydání:	2020
Předmět:	Geometric quantization Mathematics - Differential Geometry Complex system FOS: Physical sciences 01 natural sciences Mathematics - Spectral Theory symbols.namesake Operator (computer programming) 0103 physical sciences FOS: Mathematics 0101 mathematics Spectral Theory (math.SP) Quantum Mathematics::Symplectic Geometry Mathematical Physics Mathematical physics Hamiltonian mechanics Physics Parallel transport 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Differential Geometry (math.DG) Mathematics - Symplectic Geometry symbols Symplectic Geometry (math.SG) 010307 mathematical physics Hamiltonian (quantum mechanics) Symplectic geometry
Zdroj:	Letters in Mathematical Physics
ISSN:	0377-9017
DOI:	10.1007/s11005-020-01267-z
Popis:	We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized symplectic manifolds in the context of geometric quantization of Kostant and Souriau. We express the associated evolution operators via parallel transport in the quantum spaces over the induced path of almost complex structures, and we establish various semi-classical estimates. In particular, we establish a Gutzwiller trace formula for the Kostant-Souriau operator and compute explicitly the leading term. We then describe a potential application to contact topology. 36 pages. To appear in Letters in Mathematical Physics
Databáze:	OpenAIRE
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