Semiclassical limit for multistate Klein–Gordon systems: almost invariant subspaces, and scattering theory

2004 ◽  
Vol 45 (9) ◽  
pp. 3676-3696 ◽  
Author(s):  
Gheorghe Nenciu ◽  
Vania Sordoni
Keyword(s):  
Scattering Theory ◽  
Semiclassical Limit ◽  
Invariant Subspaces ◽  
Klein Gordon

scholarly journals Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary

2017 ◽  
Vol 8 (1) ◽  
pp. 559-582 ◽  
Author(s):  
Mónica Clapp ◽  
Marco Ghimenti ◽  
Anna Maria Micheletti
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Compact Riemannian Manifold ◽  
Semiclassical Limit ◽  
Arbitrary Dimension ◽  
Neumann Boundary ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Manifold With Boundary ◽  
Klein Gordon

Abstract We study the semiclassical limit to a singularly perturbed nonlinear Klein–Gordon–Maxwell–Proca system, with Neumann boundary conditions, on a Riemannian manifold {\mathfrak{M}} with boundary. We exhibit examples of manifolds, of arbitrary dimension, on which these systems have a solution which concentrates at a closed submanifold of the boundary of {\mathfrak{M}} , forming a positive layer, as the singular perturbation parameter goes to zero. Our results allow supercritical nonlinearities and apply, in particular, to bounded domains in {\mathbb{R}^{N}} . Similar results are obtained for the more classical electrostatic Klein–Gordon–Maxwell system with appropriate boundary conditions.

Semiclassical Limit of Multichannel Scattering Theory

1975 ◽  
Vol 34 (14) ◽  
pp. 849-852 ◽  
Author(s):  
John R. Laing ◽  
Karl F. Freed
Keyword(s):  
Scattering Theory ◽  
Semiclassical Limit ◽  
Multichannel Scattering

scholarly journals QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA

1993 ◽  
Vol 08 (05) ◽  
pp. 947-981 ◽  
Author(s):  
TIMOTHY HOLLOWOOD
Keyword(s):  
Scattering Theory ◽  
Matrix Theory ◽  
Semiclassical Limit ◽  
Soliton Solutions ◽  
Hecke Algebra ◽  
Quantum Field Theories ◽  
Coupling Constant ◽  
S Matrix ◽  
Restricted Region ◽  
Definition Of

The problem of quantizing a class of two-dimensional integrable quantum field theories is considered. The classical equations of the theory are the complex sl(n) affine Toda equations which admit soliton solutions with real masses. The classical scattering theory of the solitons is developed using Hirota’s solution techniques. A form for the soliton S matrix is proposed based on the constraints of S matrix theory, integrability and the requirement that the semiclassical limit is consistent with the semiclassical WKB quantization of the classical scattering theory. The proposed S matrix is an intertwiner of the quantum group associated to sl(n), where the deformation parameter is a function of the coupling constant. It is further shown that the S matrix describes a nonunitary theory, which reflects the fact that the classical Hamiltonian is complex. The spectrum of the theory is found to consist of the basic solitons, excited (or ‘breathing’) solitons, scalar states (or breathers) and solitons transforming in nonfundamental representations. For some region of coupling constant space only the original solitons are in the spectrum and so the S matrix is complete, in addition arguments are presented which indicate that in a more restricted region the theory is actually unitary. It is also noted that the construction of the S matrix is valid for any representation of the Hecke algebra, allowing the definition of restricted S matrices, which lie in the unitary and complete region.

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