Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

DOI10.1016/j.jfa.2014.08.002zbMath1298.81499arXiv1304.6662OpenAlexW2083375007MaRDI QIDQ457637

Fumio Hiroshima, Massimiliano Gubinelli, József Lörinczi

Publication date: 29 September 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.6662

zbMATH Keywords

ultraviolet cutoffFeynman-Kac representationNelson modelenergy renormalization

Mathematics Subject Classification ID

Model quantum field theories (81T10) Other elementary particle theory in quantum theory (81V25) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Statistical thermodynamics (82B30)

Related Items (14)

Ground states and associated path measures in the renormalized Nelson model ⋮ A lower bound on the renormalized Nelson model ⋮ Functional central limit theorems and \(P(\phi )_1\)-processes for the relativistic and non-relativistic Nelson models ⋮ Bogoliubov dynamics and higher-order corrections for the regularized Nelson model ⋮ Hamiltonians for polaron models with subcritical ultraviolet singularities ⋮ Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively ⋮ On the semigroup generated by the renormalized Nelson Hamiltonian ⋮ On renormalized Hamiltonian nets ⋮ Asymptotics of the evolution semigroup associated with a scalar field in the presence of a non-linear electromagnetic field ⋮ On Nelson-type Hamiltonians and abstract boundary conditions ⋮ Estimates on functional integrals of quantum mechanics and non-relativistic quantum field theory ⋮ Spin-boson model through a Poisson-driven stochastic process ⋮ Scaling limits with a removal of ultraviolet cutoffs for semi-relativistic particles system coupled to a scalar Bose field ⋮ Absence of ground states in the renormalized massless translation-invariant Nelson model

Cites Work

• Removal of UV cutoff for the Nelson model with variable coefficients
• The infrared behaviour in Nelson's model of a quantum particle coupled to a massless scalar field.
• Ground state for point particles interacting through a massless scalar Bose field
• Feynman-Kac-type theorems and Gibbs measures on path space. With applications to rigorous quantum field theory.
• Infrared catastrophe for Nelson's model -- non-existence of ground state and soft-boson divergence
• Quantum electrodynamics of confined nonrelativistic particles
• Ground state of a quantum particle coupled to a scalar Bose field
• On the existence of ground states for massless Pauli-Fierz Hamiltonians
• The Gibbs ensemble of a vortex filament
• Ground state of the massless Nelson model in a non-Fock representation
• Gibbs measures on Brownian currents
• GIBBS MEASURES WITH DOUBLE STOCHASTIC INTEGRALS ON A PATH SPACE
• Brownian motion and harnack inequality for Schrödinger operators
• GROUND STATE OF THE MASSLESS NELSON MODEL WITHOUT INFRARED CUTOFF IN A NON-FOCK REPRESENTATION
• GROUND STATE PROPERTIES OF THE NELSON HAMILTONIAN: A GIBBS MEASURE-BASED APPROACH
• Weak coupling limit and removing an ultraviolet cutoff for a Hamiltonian of particles interacting with a quantized scalar field
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