From Supersymmetric Quantum Mechanics to Scalar Field Theories

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.