Equivalent Hamiltonian for the Lee model

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.