Equivalent Hamiltonian for Lee Model

Abstract

Using the techniques of quasi-Hermitian quantum mechanics and quantum field theory we use a similarity transformation to construct an equivalent Hermitian Hamiltonian for the Lee model. In the field theory confined to the $V/Nθ$ sector it effectively decouples $V$, replacing the three-point interaction of the original Lee model by an additional mass term for the $V$ particle and a four-point interaction between $N$ and $θ$. While the construction is originally motivated by the regime where the bare coupling becomes imaginary, leading to a ghost, it applies equally to the standard Hermitian regime where the bare coupling is real. In that case the similarity transformation becomes a unitary transformation.