Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

  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},

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


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



Weak coupling limit and removing an ultraviolet cutoff for a Hamiltonian of particles interacting with a quantized scalar field

An interaction system consisting of particles and a quantized scalar field is considered. The Hamiltonian of the system is defined as a self-adjoint operator in a Hilbert space. An ultraviolet cutoff

The Infrared Behaviour in Nelson's Model of a Quantum Particle Coupled to a Massless Scalar Field

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

We consider the interaction of a finite number of nonrelativistic particles with a positive or zero mass quantum field. We show that in the weak coupling limit the quantum field gives rise to an

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


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,