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Article Dans Une Revue Communications in Mathematical Physics Année : 2011

Infrared problem for the Nelson model on static space-times

Résumé

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.
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Dates et versions

hal-00476310 , version 1 (26-04-2010)
hal-00476310 , version 2 (24-11-2010)
hal-00476310 , version 3 (03-01-2011)

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Christian Gérard, Fumio Hiroshima, Annalisa Panati, Akito Suzuki. Infrared problem for the Nelson model on static space-times. Communications in Mathematical Physics, 2011, 308 (2), pp.543-566. ⟨10.1007/s00220-011-1289-7⟩. ⟨hal-00476310v3⟩
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