Constructing Bidimensional Scalar Field Theory Models From Zero Mode Fluctuations

Abstract

In this paper we review how to reconstruct scalar field theories in two dimensional spacetime starting from solvable Schrodinger equations. Three different Schrodinger potentials are analyzed. We obtained two new models starting from the Morse and Scarf II hyperbolic potentials, {\it i.e}, the $U(\phi)=\phi^2\ln^2(\phi^2)$ model and $U(\phi)=\phi^2\cos^2(\ln(\phi^2))$ model respectively.