Nonlinear quantummechanical system associated with SineGordon equation in (1 + 2) dimensions
Despite the fact that it is not integrable, the (1 + 2)dimensional SineGordon equation has Nsoliton solutions, whose velocities are lower than the speed of light (c = 1), for all N ≥ 1. Based on these solutions, a quantummechanical system is constructed over a Fock space of particles. The coordinate of each particle is an angle around the unit circle. U, a nonlinear functional of the particle numberoperators, which obeys the SineGordon equation in (1 + 2) dimensions, is constructed. Its eigenvalues on Nparticle states in the Fock space are the slowerthanlight, Nsoliton solutions of the equation. A projection operator (a nonlinear functional of U), which vanishes on the singleparticle subspace, is a massdensity generator. Its eigenvalues on multiparticle states play the role of the mass density of structures that emulate free, spatially extended, relativistic particles. The simplicity of the quantummechanical system allows for the incorporation of perturbations with particle interactions, which have the capacity to “annihilate” and “create” solitons – an effect that does not have an analog in perturbed classical nonlinear evolution equations.
 Authors:

^{[1]}
 Jacob Blaustein Institutes for Desert Research, BenGurion University of the Negev, Midreshet BenGurion, 8499000 (Israel)
 Publication Date:
 OSTI Identifier:
 22305868
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PARTICLE INTERACTIONS; PERTURBATION THEORY; PROJECTION OPERATORS; QUANTUM MECHANICS; RELATIVISTIC RANGE; SINEGORDON EQUATION