Infrared problem for the Nelson model on static space-times

Abstract

We consider the Nelson model with variable coefficients and investigate the problem of existence of a ground state and the removal of the ultraviolet cutoff. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. A physical example is obtained by quantizing the Klein-Gordon equation on a static space-time coupled with a non-relativistic particle. We investigate the existence of a ground state of the Hamiltonian in the presence of the infrared problem, i.e. assuming that the boson mass tends to 0 at infinity.

References in corpus (2)

• Spectral and scattering theory for some abstract QFT Hamiltonians
• Absence of ground state for the Nelson model on static space-times

Cited by in corpus (8)

• Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy
• Self-Adjointness criterion for operators in Fock spaces
• Removal of UV cutoff for the Nelson model with variable coefficients
• Ground State Properties in the Quasi-Classical Regime
• Bohr's correspondence principle in quantum field theory and classical renormalization scheme: the Nelson model
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• Functional central limit theorems and $P(phi{)}_1$-processes for the classical and relativistic Nelson models
• Existence of a ground state for the Nelson model with a singular perturbation