Avoiding Ultraviolet Divergence by Means of Interior–Boundary Conditions

DOI10.1007/978-3-319-26902-3_14zbMath1338.81296arXiv1506.00497OpenAlexW585342573WikidataQ62036690 ScholiaQ62036690MaRDI QIDQ2800040

Roderich Tumulka, Stefan Teufel

Publication date: 14 April 2016

Published in: Quantum Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.00497

zbMATH Keywords

Schrödinger operatorboundary conditionself-adjointnessparticle creation and annihilationregularization of quantum field theoryultraviolet infinity

Mathematics Subject Classification ID

Model quantum field theories (81T10) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Time-dependent Schrödinger equations and Dirac equations (35Q41) Initial-boundary value problems for linear first-order PDEs (35F16)

Related Items (16)

Interior-boundary conditions for the Dirac equation at point sources in three dimensions ⋮ Complex charges, time reversal asymmetry, and interior-boundary conditions in quantum field theory ⋮ Interior-boundary conditions for Schrödinger operators on codimension-1 boundaries ⋮ Consistency of multi-time Dirac equations with general interaction potentials ⋮ The resolvent of the Nelson Hamiltonian improves positivity ⋮ Particle creation at a point source by means of interior-boundary conditions ⋮ Characterization of efficient solutions for a class of PDE-constrained vector control problems ⋮ Creation rate of Dirac particles at a point source ⋮ Self-adjointness of a class of multi-spin-boson models with ultraviolet divergences ⋮ Multi-time formulation of particle creation and annihilation via interior-boundary conditions ⋮ Bohmian trajectories for Hamiltonians with interior-boundary conditions ⋮ The renormalized Bogoliubov–Fröhlich Hamiltonian ⋮ Constrained variational problems governed by second-order Lagrangians ⋮ On Nelson-type Hamiltonians and abstract boundary conditions ⋮ A nonrelativistic quantum field theory with point interactions in three dimensions ⋮ Bohmian mechanics at space-time singularities. I: Timelike singularities

Cites Work

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• Van Hove Hamiltonians -- exactly solvable models of the infrared and ultraviolet problem
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• Quantum theory of the diplon
• Time-evolution of the external field problem in Quantum Electrodynamics
• Les difficultés de divergences pour un modèle particulier de champ quantifié
• Some Special Examples in Renormalizable Field Theory

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