Construction of (1+1)-Dimensional Field Models with Exactly Solvable Fluctuation Equations about Classical Finite-Energy Configurations

Abstract

A systematic construction of (1+1)-dimensional field theoretic models with exactly solvable excitation spectrum about its classical static finite-energy configuration is presented. The approach is based on the concept of shape-invariant potentials in supersymmetric quantum mechanics. Stable and unstable field models are taken into account. In the case of stable models two new field potentials are found, which give rise to exactly solvable fluctuation equations about their topologically non-trivial classical solutions. In the case of unstable models two new families of field potentials with fractional powers and one with a logarithmic term are found.