Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

@article{Gubinelli2013UltravioletRO,
  title={Ultraviolet renormalization of the Nelson Hamiltonian through functional integration},
  author={Massimiliano Gubinelli and Fumio Hiroshima and J{\'o}zsef Lőrinczi},
  journal={Journal of Functional Analysis},
  year={2013},
  volume={267},
  pages={3125-3153}
}
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23 Citations
Highly Influential Citations
3
Background Citations
5
Methods Citations
6
Results Citations
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23 Citations

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…

Ultraviolet Renormalisation of a quantum field toy model I

We consider a class of Hamiltonians describing a fermion field coupled to a boson field. The interaction kernels are assumed bounded in the fermionic momentum variable and decaying like |q| for large…

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…

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…

Hamiltonians for polaron models with subcritical ultraviolet singularities

We treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity,…

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…

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…

Absence of Ground States in the Renormalized Massless Translation-Invariant Nelson Model

We consider the model of a massive non-relativistic spinless particle interacting with a massless bosonic field, widely referred to as the Nelson model. It is well known, that a UV renormalized…

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…

Feynman-Kac formulas for the ultra-violet renormalized Nelson model

We derive Feynman-Kac formulas for the ultra-violet renormalized Nelson Hamiltonian with a Kato decomposable external potential and for corresponding fiber Hamiltonians in the translation invariant…

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