The mass shell in the semi-relativistic Pauli-Fierz model

Abstract

We consider the semi-relativistic Pauli-Fierz model for a single free electron interacting with the quantized radiation field. Employing a variant of Pizzo's iterative analytic perturbation theory we construct a sequence of ground state eigenprojections of infra-red cutoff, dressing transformed fiber Hamiltonians and prove its convergence, as the cutoff goes to zero. Its limit is the ground state eigenprojection of a certain Hamiltonian unitarily equivalent to a renormalized fiber Hamiltonian acting in a coherent state representation space. The ground state energy is an exactly two-fold degenerate eigenvalue of the renormalized Hamiltonian, while it is not an eigenvalue of the original fiber Hamiltonian unless the total momentum is zero. These results hold true, for total momenta inside a ball about zero of arbitrary radius p>0, provided that the coupling constant is sufficiently small depending on p and the ultra-violet cutoff. Along the way we prove twice continuous differentiability and strict convexity of the ground state energy as a function of the total momentum inside that ball.

44 pages

References in corpus (7)

• Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED
• Effective dynamics of an electron coupled to an external potential in non-relativistic QED
• Analyticity of The Ground State Energy For Massless Nelson Models
• On the ionization energy of the semi-relativistic Pauli-Fierz model for a single particle
• Ground states of semi-relativistic Pauli-Fierz and no-pair Hamiltonians in QED at critical Coulomb coupling
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• Ultraviolet Properties of the Spinless, One-Particle Yukawa Model

Cited by in corpus (11)

• Absence of Ground States in the Renormalized Massless Translation-Invariant Nelson Model
• Coulomb scattering in the massless Nelson model III. Ground state wave functions and non-commutative recurrence relations
• On enhanced binding and related effects in the non- and semi-relativistic Pauli-Fierz models
• Self-adjointness of semi-relativistic Pauli-Fierz Hamiltonian
• Curing velocity superselection in non-relativistic QED by restriction to a lightcone
• Relative normalizers of automorphism groups, infravacua and the problem of velocity superselection in QED
• A soft-photon theorem for the Maxwell-Lorentz system
• Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively
• Ultraviolet Properties of the Spinless, One-Particle Yukawa Model
• Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition
• Ground States for Infrared Renormalized Translation-Invariant Non-Relativistic QED