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. 
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Methods Citations
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13 Citations

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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…
Ultraviolet renormalization of the Nelson Hamiltonian through functional integration
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…
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References

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