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

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
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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…
Renormalized Nelson model
In this paper renormalized Nelson Hamiltonian in quantum field theory is discussed. Gibbs measure associated with the ground state of the Nelson Hamiltonian is constructed, and the super exponential…
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…
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References

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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…
Scattering Theory of Infrared Divergent Pauli-Fierz Hamiltonians
Abstract. We consider in this paper the scattering theory of infrared divergent massless Pauli-Fierz Hamiltonians. We show that the CCR representations obtained from the asymptotic field contain…
Particle–boson interactions and the weak coupling limit
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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…
Ground state of the massless Nelson model without infrared cutoff in a non-Fock representation
We consider a model of quantum particles coupled to a massless quantum scalar field, called the massless Nelson model, in a non-Fock representation of the time-zero fields which satisfy the canonical…
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…
QUANTUM ELECTRODYNAMICS OF CONFINED NONRELATIVISTIC PARTICLES
Abstract We consider a system of finitely many nonrelativistic, quantum mechanical electrons bound to static nuclei. The electrons are minimally coupled to the quantized electromagnetic field; but we…
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…
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,…
Effective mass of the polaron: a functional integral approach
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