Constructing Bidimensional Scalar Field Theory Models From Zero Mode Fluctuations

TL;DR

This paper reviews methods to reconstruct two-dimensional scalar field theories from solvable Schrödinger equations, introducing two new models derived from Morse and Scarf II potentials.

Contribution

It presents a novel approach to construct scalar field models using zero mode fluctuations and introduces two new models based on specific solvable potentials.

Findings

Derived two new scalar field models from Morse and Scarf II potentials.

Demonstrated the reconstruction process from Schrödinger equations to field theories.

Expanded the set of known solvable scalar field models.

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.