# From Supersymmetric Quantum Mechanics to Scalar Field Theories

## TL;DR

This paper explores how to reconstruct scalar field theories from supersymmetric quantum mechanics, revealing that uniqueness depends on the number of bound states, with potential for multiple theories from the same quantum system.

## Contribution

It demonstrates the reconstruction process from reflectionless potentials and shows that multiple field theories can emerge from the same quantum mechanical setup when two bound states are involved.

## Key findings

- Reconstruction is unique for single bound state potentials.
- Multiple field theories can arise from two bound state potentials.
- The method applies to reflectionless potentials with one or two bound states.

## Abstract

In this work we address the reconstruction problem, investigating the construction of field theories from supersymmetric quantum mechanics. The procedure is reviewed, starting from reflectionless potentials that admit one and two bound states. We show that, although the field theory reconstructed from the potential that support a single bound state is unique, it may break unicity in the case of two bound states. We illustrate this with an example, which leads us with two distinct field theories.