A probabilistic representation of the ground state expectation of fractional powers of the boson number operator

DOI10.1016/j.jmaa.2012.04.076zbMath1252.81091arXiv1105.1850OpenAlexW2008722406MaRDI QIDQ448229

Fumio Hiroshima, Toshimitsu Takaesu, József Lörinczi

Publication date: 30 August 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.1850

zbMATH Keywords

ground stateNelson modelboson number operatorGibbs measure on path spacerandom-time Poisson process

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Path integrals in quantum mechanics (81S40) Many-body theory; quantum Hall effect (81V70) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31)

Related Items (1)

Ground states and associated path measures in the renormalized Nelson model

Cites Work

• Unnamed Item
• 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
• A central limit theorem for Gibbs measures relative to Brownian motion
• Scattering theory of infrared divergent Pauli-Fierz Hamiltonians
• Approach to ground state and time-independent photon bound for massless spin-boson models
• Fiber Hamiltonians in non-relativistic quantum electrodynamics
• PATH INTEGRAL REPRESENTATION FOR SCHRÖDINGER OPERATORS WITH BERNSTEIN FUNCTIONS OF THE LAPLACIAN
• Ground state of the massless Nelson model in a non-Fock representation
• 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

This page was built for publication: A probabilistic representation of the ground state expectation of fractional powers of the boson number operator