Inelastic kink-antikink collisions are investigated in the two-dimensional ¢' model. It is shown that a bound state of the kink and antikink is formed when the colliding velocity V is less than a critical V" and that inelastic scattering of the kinks is caused when V> V,. These phenomena are due to the excitation of internal modes of the kinks. An excited kink is not stable but emits bosuns to decay into the ground state kink. Numerical calculations were also performed for classical kink-antikink collision processes. § 1. Introduction A large class of non-linear field equations has localized stable soh;tions which are called solitons. The quantum theory of soliton has been studied by many authors aiming at constructing a model of extended particles. Semi-classical methods have been applied to the quantization of a soliton and the systematic perturbation theories have been developed at least in one-soliton sector.n' 2 ' However, we have no satisfactory treatment of the quantum scattering of solitons. 3 l In the strict meaning used in mathematical literature, solitons are stable even against collisions. Since this stability is guaranteed by an infinite number of conserved quantities,·') these solitons are scattered elastically also in quantum theory. The sine-Gordon model provides a good example of such solitons. In particle physics, however, it may be useful to understand solitons in a broad sense. That is, if a field equation has a classical solution vvhose energy is localized in a finite volume and which is stable against small fiuctional variations, we call it a soliton solution. In this sense, there are solitons which are unstable against a collision, and it is important to study inelastic scattering of such solitons. In this paper, we investigate soliton-antisoliton collision processes m the two-dimensional ¢ 4 model as an example of the inelastic scattering of solitons. The two-dimensional ¢ 4 model has the so-called kink solutions and a fluctuation mode trapped in the kink. The kinks are scattered inelastically because of the excitation of the internal modes. In § § 2 and 3, we introduce a collective coordinate into a kink-antikink system and derive the equations of motion for the system. Solving the equations approximately, we estimate the excitation probability of the internal
CITATION STYLE
Sugiyama, T. (1979). Kink-Antikink Collisions in the Two-Dimensional 4 Model. Progress of Theoretical Physics, 61(5), 1550–1563. https://doi.org/10.1143/ptp.61.1550
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