On Nelson-type Hamiltonians and abstract boundary conditions

Abstract

We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms of boundary conditions that relate sectors with different numbers of bosons. We treat both models in which the Hamiltonian may be defined as a form perturbation of the free operator, such as Fröhlich's polaron, and renormalisable models, such as the massive Nelson model.

arXiv commentv3 accepted for publication in CMP

References in corpus (13)

• Multiparticle Schrodinger operators with point interactions in the plane
• Self-Adjointness and Domain of the Froehlich Hamiltonian
• A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity
• Avoiding Ultraviolet Divergence by Means of Interior-Boundary Conditions
• On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians
• On the domain of the Nelson Hamiltonian
• Particle Creation at a Point Source by Means of Interior-Boundary Conditions
• Stability of a fermionic $N+1$ particle system with point interactions
• Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy
• Particle creation and annihilation at interior boundaries: One-dimensional models
• Stability of the 2+2 fermionic system with point interactions
• Spectral theory for Schrödinger operators with $\delta$-interactions supported on curves in ${\mathbb{R}}^3$
• Stability of the two-dimensional Fermi polaron

Cited by in corpus (27)

• Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
• The Renormalised Bogoliubov-Fröhlich Hamiltonian
• A nonrelativistic quantum field theory with point interactions in three dimensions
• Multi-time formulation of particle creation and annihilation via interior-boundary conditions
• On a Direct Description of Pseudorelativistic Nelson Hamiltonians
• Ground states and associated path measures in the renormalized Nelson model
• A note on the Fröhlich dynamics in the strong coupling limit
• On the self-adjointness of H+A*+A
• Bohmian Trajectories for Hamiltonians with Interior-Boundary Conditions
• Absence of Ground States in the Renormalized Massless Translation-Invariant Nelson Model
• On the global minimum of the energy-momentum relation for the polaron
• Self-adjointness of a class of multi-spin-boson models with ultraviolet divergences
• Interior-Boundary Conditions for Many-Body Dirac Operators and Codimension-1 Boundaries
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• The resolvent of the Nelson Hamiltonian improves positivity
• Interior-Boundary Conditions for the Dirac Equation at Point Sources in 3 Dimensions
• Hamiltonians for polaron models with subcritical ultraviolet singularities
• Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively
• Interior-Boundary Conditions for Schrodinger Operators on Codimension-1 Boundaries
• Boundary Conditions that Remove Certain Ultraviolet Divergences
• Extended State Space for describing renormalized Fock spaces in QFT
• A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate
• Renormalization of spin$\unicode{x2013}$boson interactions mediated by singular form factors
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
• Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
• On the resolvent of $H+A^{\ast }+A$
• Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition