Nonminimal particle-like solutions in cubic scalar field theory

TL;DR

This paper investigates the properties of bell-shaped solitary wave solutions in cubic scalar field theory, exploring their quantization, symmetry, and quantum mass corrections, revealing novel quantum features beyond perturbation theory.

Contribution

It demonstrates the quantization of these solutions with higher derivatives, uncovers an SU(2) symmetry, and computes quantum mass corrections not accessible via standard perturbation methods.

Findings

Quantum equation exhibits SU(2) symmetry.

Quantum corrections to mass are computed beyond perturbation theory.

Nonminimal p-brane action is ruled out for these solutions.

Abstract

The cubic scalar field theory admits the bell-shaped solitary wave solutions which can be interpreted as massive Bose particles. We rule out the nonminimal p-brane action for such a solution as the point particle with curvature. When quantizing it as the theory with higher derivatives, it is shown that the corresponding quantum equation has SU(2) dynamical symmetry group realizing the exact spin-coordinate correspondence. Finally, we calculate the quantum corrections to the mass of the bell boson which can not be obtained by means of the perturbation theory starting from the vacuum sector.