Ground States for Infrared Renormalized Translation-Invariant Non-Relativistic QED

Abstract

We consider a translation-invariant Pauli-Fierz model describing a non-relativistic charged quantum mechanical particle interacting with the quantized electromagnetic field. The charged particle may be spinless or have spin one half. We decompose the Hamiltonian with respect to the total momentum into a direct integral of so called fiber Hamiltonians. We perform an infrared renormalization, in the sense of norm resolvent convergence, for each fiber Hamiltonian, which has the physical interpretation of removing an infinite photon cloud. We show that the renormalized fiber Hamiltonians have a ground state for almost all values for the total momentum with modulus less than one.

arXiv comment42 pages

References in corpus (11)

• Ground States in Non-relativistic Quantum Electrodynamics
• Infraparticle Scattering States in Non-Relativistic QED: I. The Bloch-Nordsieck Paradigm
• On the self-adjointness and domain of Pauli-Fierz type Hamiltonians
• Infraparticle Scattering States in Non-Relativistic QED: II. Mass Shell Properties
• Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED
• Analyticity of The Ground State Energy For Massless Nelson Models
• The mass shell in the semi-relativistic Pauli-Fierz model
• On Existence of Ground States in the Spin Boson Model
• Coulomb scattering in the massless Nelson model I. Foundations of two-electron scattering
• Ground States for translationally invariant Pauli-Fierz Models at zero Momentum
• Relative normalizers of automorphism groups, infravacua and the problem of velocity superselection in QED