• Corpus ID: 237372106

The Nelson Model on Static Spacetimes

@inproceedings{Kruse2021TheNM,
  title={The Nelson Model on Static Spacetimes},
  author={Jan Philipp Kruse and Jonas Lampart},
  year={2021}
}
The Nelson model describes the interaction of nonrelativistic quantum particles with a relativistic quantum field of scalar bosons. Nelson rigorously demonstrated in 1964 the existence of a well-defined self-adjoint Nelson Hamiltonian by renormalisation. Recently, a Fock space description of the renormalised Nelson Hamiltonian and its domain were found based on a novel approach to defining Hamiltonians in quantum field theories. This novel approach involves an interior boundary condition (IBC… 

References

SHOWING 1-10 OF 14 REFERENCES
Interaction of Nonrelativistic Particles with a Quantized Scalar Field
We demonstrate the mathematical existence of a meson theory with nonrelativistic nucleons. A system of Schrodinger particles is coupled to a quantized relativistic scalar field. If a cutoff is put on
Infrared Problem for the Nelson Model on Static Space-Times
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
On a direct description of pseudorelativistic Nelson Hamiltonians
Abstract interior-boundary conditions (IBC's) allow for the direct description of the domain and the action of Hamiltonians for a certain class of ultraviolet-divergent models in Quantum Field
On Nelson-Type Hamiltonians and Abstract Boundary Conditions
We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation
Hamiltonians without ultraviolet divergence for quantum field theories
We propose a way of defining Hamiltonians for quantum field theories without any renormalization procedure. The resulting Hamiltonians, called IBC Hamiltonians, are mathematically well defined (and
On the domain of the Nelson Hamiltonian
The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper
Avoiding Ultraviolet Divergence by Means of Interior–Boundary Conditions
We describe here a novel way of defining Hamiltonians for quantum field theories (QFTs), based on the particle–position representation of the state vector and involving a condition on the state
Self-adjointness and domain of the Fröhlich Hamiltonian
In the large polaron model of Herbert Frohlich, the electron-phonon interaction is a small perturbation in form sense, but a large perturbation in operator sense. This means that the form-domain of
Adiabatic perturbation theory in quantum dynamics
Introduction.- First-order adiabatic theory.- Space-adiabatic perturbation theory.- Applications and extensions.- Quantum dynamics in periodic media.- Adiabatic decoupling without spectral gap.-
Removal of UV Cutoff for the Nelson Model with Variable Coefficients
We consider the Nelson model with variable coefficients. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric,
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