2010/12/13 by Christian Gérard, Fumio Hiroshima, Gérard, Christian +5
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum Chromodynamics and Particle Interactions #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.1012.2655
We consider the Nelson model on some static space-times and investigate the problem of absence of a ground state. 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. We investigate the absence of a ground state of the Hamiltonian in the presence of the infrared problem, i.e. assuming that the boson mass m(x) tends to 0 at spatial infinity. Using path space techniques, we show that if m(x)≤ C |x|-μ at infinity for some C>0 and μ>1 then the Nelson Hamiltonian has no ground state.