Equivalent Hamiltonian for the Lee model

2007/11/30 by H. F. Jones · 3 citations
Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th

paper · pdf · doi:10.1103/physrevd.77.065023

published as Phys.Rev.D77:065023,2008 · 9 pages, no figures

arxiv created 2007/11/30 · openalex publication_date 2008/03/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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\ensuremathθ 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 \ensuremathθ. 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.

Citations

• ExactPT-symmetry is equivalent to Hermiticity

Cited by

• Some spectral equivalences between Schrödinger operators
• Exactly solvablePT-symmetric Hamiltonian having no Hermitian counterpart
• Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions

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