2004/06/22 by Andrew Beckwith, A. W. Beckwith, Beckwith, A. W.
Mathematics · Physics and Astronomy · #False vacuum #Hamiltonian (control theory) #Inequality #Law #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Physics #Political science #Quantum Mechanics and Applications #Quantum mechanics #Quantum tunnelling #Representation (politics) #Spectral Theory in Mathematical Physics #Statistical physics #Theoretical physics #advanced mathematical theories #math-ph #math.MP #msc:34A40 #msc:81T99
paper · pdf · doi:10.48550/arxiv.math-ph/0406048
34 pages,one figure; major re dos to put paper in format expected of APS sytle manual, plus nine pages of verbal explanations, clarifications put in due to interaction with referees who gave constructive criticism of the format style
openalex publication_date 2004/06/22 · arxiv created 2004/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The tunneling Hamiltonian has proven to be a useful method in many body physics to treat particle tunneling between different states represented as wave functions. Here we present a generalization of the tunneling Hamiltonian to quantum field theory, in which tunneling between states represented as wave functionals of a scalar quantum field is considered. We examine quantum decay of the false vacuum in the driven Sine-Gordon system, and show it is consistent with the tunneling formalism derived here and matches up with the soliton - anti soliton separation obtained from the Bogomil'nyi inequality. This inequality permits construction of a gaussian wave functional representation of soliton - anti soliton nucleated states and is consistent with respect to the false vacuum hypothesis