Constructing bidimensional scalar field theory models from zero mode fluctuations

In this paper we review how to construct scalar field theories in two-dimensional space-time that support kink or bouncelike solutions starting from solvable Schr\"odinger equations. Three different Schr\"odinger potentials are analyzed. We obtain two new models starting from the Morse and Scarf II hyperbolic potentials, i.e. the $U(\ensuremath{\varphi})={\ensuremath{\varphi}}^{2}{\mathrm{ln}}^{2}({\ensuremath{\varphi}}^{2})$ and $U(\ensuremath{\varphi})={\ensuremath{\varphi}}^{2}{\mathrm{cos}}^{2}\mathrm{ln}({\ensuremath{\varphi}}^{2})$ models, respectively. Also we give a closed expression for the (renormalized) kink quantum mass corrections in the case of the second model and evaluate it numerically.