Equivalent Hamiltonian for Lee Model

TL;DR

This paper constructs an equivalent Hermitian Hamiltonian for the Lee model using quasi-Hermitian quantum mechanics, transforming the interaction into mass and four-point terms, applicable in both ghost and standard regimes.

Contribution

It introduces a similarity transformation to derive an equivalent Hermitian Hamiltonian for the Lee model, clarifying its structure in different coupling regimes.

Findings

Effective decoupling of V in the field theory sector

Transformation replaces three-point interaction with mass and four-point terms

Applicable to both ghost and Hermitian regimes

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 $V/N\theta$ 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 $\theta$. 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.