CLASSICAL AND QUANTUM COMPARISON OF KINK AND BELL SOLITONS AS ZERO-BRANES

Abstract

The self-interacting scalar field theory with the negative coupling constant gives rise to the bell-shaped solitary wave solution which can be interpreted as a massive Bose particle. We compare its properties with those of the kink solution (also known as the domain-wall potential) arisen in the theory with the positive constant introducing the simplest example of the spontaneous breaking of symmetry. We rule out the uniform p-brane action for the kink and bell solutions as the nonminimal point particles with curvature. When quantizing it as the theory with higher derivatives, it is shown that the appearing quantum equation has SU (2) dynamical symmetry group realizing the exact spin-coordinate correspondence. Finally, we calculate the quantum corrections to the masses of kink and bell bosons which cannot be obtained by means of the perturbation theory starting from the vacuum sector.