Nonlinear quantum-mechanical system associated with Sine-Gordon equation in (1+2) dimensions

作者：Zarmi Yair^*

来源：Journal of Mathematical Physics, 2014, 55(10): 103510.

DOI：10.1063/1.4899085

Despite the fact that it is not integrable, the (1 + 2)-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N %26gt;= 1. Based on these solutions, a quantum-mechanical 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 number-operators, which obeys the Sine-Gordon equation in (1 + 2) dimensions, is constructed. Its eigenvalues on N-particle states in the Fock space are the slower-than-light, N-soliton solutions of the equation. A projection operator (a nonlinear functional of U), which vanishes on the single-particle subspace, is a mass-density generator. Its eigenvalues on multi-particle states play the role of the mass density of structures that emulate free, spatially extended, relativistic particles. The simplicity of the quantum-mechanical system allows for the incorporation of perturbations with particle interactions, which have the capacity to %26quot;annihilate%26quot; and %26quot;create%26quot; solitons-an effect that does not have an analog in perturbed classical nonlinear evolution equations.

• 出版日期2014-10