On the geometry of slow-fast phase spaces and the semiclassical quantization. (English) Zbl 1470.53073
The paper under review concerns applications of the torus quantization results to a class of pseudodifferential operators depending on two small parameters. More precisely, the adiabatic-type sitution is studied, when the phase space splits into slow and fast parts and typically arises under some special relations between the given parameters \(h_1\ll h_2\ll 1\). The considered relationship between the parameters is \(h_2=\hbar \), \(h_1=\varepsilon \hbar\) where \(\hbar \ll 1\) and \(\varepsilon \ll 1\) play the role of the semiclassical and classical adiabatic parameter respectively.
Reviewer: Mircea Crâşmăreanu (Iaşi)
MSC:
| 53D50 | Geometric quantization |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
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