Removal of UV Cutoff for the Nelson Model with Variable Coefficients

@article{Grard2012RemovalOU,
  title={Removal of UV Cutoff for the Nelson Model with Variable Coefficients},
  author={Christian G{\'e}rard and Fumio Hiroshima and Annalisa Panati and Akito Suzuki},
  journal={Letters in Mathematical Physics},
  year={2012},
  volume={101},
  pages={305-322}
}
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, allowing also the boson mass to depend on position. We study the removal of the ultraviolet cutoff. 
Translation invariant models in QFT without ultraviolet cutoffs
The translation invariant model in quantum field theory is considered by functional integrations. Ultraviolet renormalization of the translation invariant Nelson model with a fixed total momentum is
Integral kernels of the renormalized Nelson Hamiltonian
  • Fumio
  • Physics, Mathematics
  • 2019
In this article we consider the ground state of the renormalized Nelson Hamiltonian in quantum field theory by using the integral kernel of the semigroup generated by the Hamiltonian. By introducing
Note on ultraviolet renormalization and ground state energy of the Nelson model
Ultraviolet (UV) renormalization of the Nelson model He in quantum field theory is considered. E. Nelson proved that lime!0e T(H" E ren " ) converges to e THren in [Nel64a]. A relationship between a
69 INTEGRAL KERNELS OF THE RENORMALIZED NELSON HAMILTONIAN
In this article we consider the ground state of the renormalized Nelson Hamil‐ tonian in quantum field theory by using the integral kernel of the semigroup gen‐ erated by the Hamiltonian. By
The Nelson Model on Static Spacetimes
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
Functional Central Limit Theorems and P(ϕ)1-Processes for the Relativistic and Non-Relativistic Nelson Models
We construct P(ϕ)1-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field
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
Functional central limit theorems and $P(phi)_{1}$-processes for the classical and relativistic Nelson models
We construct $P(phi)_1$-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum
The Nelson model on static Lorentzian manifolds
We are concerned with the Nelson model defined on static Lorentzian manifolds. Static Lorentzian manifold is defined by a Lorentzian manifold with a metric depending on position but independent of
...
...

References

SHOWING 1-7 OF 7 REFERENCES
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
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
Infrared Divergence of a Scalar Quantum Field Model on a Pseudo Riemannian Manifold
A scalar quantum field model defined on a pseudo Riemannian manifold is considered. The model is unitarily transformed to the one with a variable mass. By means of a Feynman-Kac-type formula, it is
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
Scattering theory of classical and quantum N-particle systems
0. Introduction.- 1. Classical Time-Decaying Forces.- 2. Classical 2-Body Hamiltonians.- 3. Quantum Time-Decaying Hamiltonians.- 4. Quantum 2-Body Hamiltonians.- 5. Classical N-Body Hamiltonians.- 6.