Infrared Problem for the Nelson Model on Static Space-Times

@article{Grard2011InfraredPF,
  title={Infrared Problem for the Nelson Model on Static Space-Times},
  author={Christian G{\'e}rard and Fumio Hiroshima and Annalisa Panati and Akito Suzuki},
  journal={Communications in Mathematical Physics},
  year={2011},
  volume={308},
  pages={543-566}
}
We consider the Nelson model on some static space-times and investigate the problem of existence 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 existence 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. We show that if… 
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References

SHOWING 1-10 OF 53 REFERENCES
The Infrared Behaviour in Nelson's Model of a Quantum Particle Coupled to a Massless Scalar Field
Abstract. We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian has no ground state in Fock space and thus it is not
Infrared Catastrophe for Nelson's Model-Non-Existence of Ground State and Soft-Boson Divergence-
We mathematically study the infrared catastrophe for the Hamiltonian of Nelson’s model when it has the external potential in a general class. For the model, we prove the pull-through formula on
Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model
Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure
Ground state properties of the Nelson Hamiltonian: A Gibbs measure-based approach
The Nelson model describes a quantum particle coupled to a scalar Bose field. We study properties of its ground state through functional integration techniques in case the particle is confined by an
On the absence of eigenvectors of Hamiltonians in a class of massless quantum field models without infrared cutoff
A class of models of quantized, massless Bose fields, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal.151 (1997), 455–503) is considered. Theorems on the absence of
Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
Time-dependent scattering theory for a large class of translation invariant models, including the Nelson and Polaron models, restricted to the vacuum and one-particle sectors is studied. We formulate
On the Hawking effect
In terms of the Painlev´e-Gullstrand-Lemaˆıtre coordinates a rather general scenario for the gravitational collapse of an object and the subsequent formation of a horizon is described by a manifestly
On the Existence of Ground States for Massless Pauli-Fierz Hamiltonians
We consider in this paper the problem of the existence of a ground state for a class of Hamiltonians used in physics to describe a confined quantum system (”matter”) interacting with a massless
...
...