Constituent quantization of soliton fields. I: Canonical action-angle formalism for the sine-Gordon system. II: Nonlinear Schrödinger system. (English) Zbl 0575.35086

Garbaczewski, Piotr

Univ. Bielefeld, Forschungszentr. Bielefeld-Bochum-Stochastik 53, 23 p. (1985).

It is well known that quantization of classical Hamiltonians is an ambiguous, coordinate-dependent procedure. The paper in question gives this problem a new setting: quantization in the action-angle variables (i.e., in a sense, canonical, constituent) is developed and investigated for completely integrable systems.
The two model cases discussed are the soliton fields in sine-Gordon and nonlinear Schrödinger equations. The energy spectra obtained after quantization are claimed to conform with those traditionally obtained by the radiation contribution is automatically accounted for the constituent quantization scheme.

Reviewer: A.Bocharov

MSC:

35Q99	Partial differential equations of mathematical physics and other areas of application
81T08	Constructive quantum field theory
81R30	Coherent states
81U99	Quantum scattering theory

Keywords:

quantization; classical Hamiltonians; action-angle variables; completely integrable systems; soliton fields; sine-Gordon; nonlinear Schrödinger; energy spectra