Enhanced Binding in Non-Relativistic QED

Abstract

We consider a Pauli-Fierz Hamiltonian for a particle coupled to a photon field. We discuss the effects of the increase of the binding energy and enhanced binding through coupling to a photon field, and prove that both effects are the results of the existence of the ground state of the self-energy operator with total momentum P = 0.

Quantitative estimates on the enhanced binding for the Pauli-Fierz operator

“…As in all previous papers [9,6,3,2,4], our method is asymptotic in α. Therefore, the problem of establishing the enhanced binding effect and estimating its strength for the physical value of α ≈ 1/137 still remains open.…”

“…Dressing a charged particle with photons increases the ability of a potential to confine it. For the Pauli-Fierz operator which describes a nonrelativistic particle interacting with a radiation field, this effect was proved for small values of the fine structure constant α, first under the simplifying assumption that the spin of the particle is absent [9], and later generalized to the case of a particle with spin [6,3]. In [2], it was shown that the effect of the enhanced binding is asymptotically small in α in the sense that the binding threshold for the Pauli-Fierz operator tends to the binding threshold for the corresponding Schrödinger operator as α tends to zero.…”

On the ground state energy of the translation invariant Pauli-Fierz model

“…The leading term of the ground state energy was demonstrated to be of order O(α 2 ) (up to normal ordering) in [8], and explicitly determined, with a rigorous error bound of order O(α 3 ). A similar result was subsequently obtained for the spin 1 2 case in [4].…”

Absence of Ground States of Generalized Spin-Boson Models

“…They showed that there exists a constant α * such that the enhanced binding occurs for arbitrary values of coupling constants |α| > α * . Hainzl, Vougalter and Vugalter [7] proved that there exists a sufficiently small constant ρ > 0 such that the enhanced binding occurs for all α ∈ (0, ρ] in the Pauli-Fierz model without the dipole approximation. Benguria and Vugalter [4] showed that the enhanced binding does not occur for sufficiently small coupling constants in the Pauli-Fierz model.…”