Ground state of the massless Nelson model in a non-Fock representation

Abstract

We consider a model of a particle coupled to a massless scalar field (the massless Nelson model) in a non-Fock representation. We prove the existence of a ground state of the system, applying the mothod of Griesemer, Lieb and Loss.

Analyticity of the Ground State Energy for Massless Nelson Models

“…That result is based on operator theoretic renormalization and requires the Hamiltonian to satisfy a mild IR-condition. By working in an IR-regular representation of the CCR, [6,30], the Hamiltonian has sufficiently regular IR-behavior, for [20] to be applicable, while its minimal energy remains unchanged (we thank the referee for pointing this out to us).…”

Enhanced binding of an N-particle system interacting with a scalar bose field I

“…The conditions (ii)-(iv) are required to verify these procedures in the proof of Proposition 2.6. See [37] for the detail. Finally (v) is an infrared regular condition and it is used to define operator T in (2.3).…”

“…Namely they show the existence of ground states of H for arbitrary values of α, but external potentials are assumed to be confined. Sasaki [37] extended [19,38] to a class of general external potentials, including the Coulomb potential.…”

A probabilistic representation of the ground state expectation of fractional powers of the boson number operator

“…It is well known that H has a unique strictly positive ground state ϕ g ∈ L 2 (R d ) ⊗ F for every g ∈ R whenever ν > 0 [4][5][6][7][8][9], and it has no ground state in this space if ν = 0 [10][11][12] unless (1.12) holds, imposing an infrared condition. Throughout this paper we assume that ν > 0.…”