Renormalized interaction of relativistic bosons with delta function potentials

DOI10.1063/1.3456122zbMath1312.81112arXiv0912.0377OpenAlexW1530034603MaRDI QIDQ5253692

Çağlar Doǧan, O. Teoman Turgut

Publication date: 27 May 2015

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

Full work available at URL: https://arxiv.org/abs/0912.0377

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Operations with distributions and generalized functions (46F10) Strong interaction, including quantum chromodynamics (81V05) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Quantum field theory on curved space or space-time backgrounds (81T20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Geodesics in global differential geometry (53C22) Heat kernel (35K08)

Related Items (6)

On the number of bound states of point interactions on hyperbolic manifolds ⋮ A Klein-Gordon particle captured by embedded curves ⋮ Unnamed Item ⋮ Existence of Hamiltonians for some singular interactions on manifolds ⋮ Non-relativistic Lee model in two-dimensional Riemannian manifolds ⋮ Born-Oppenheimer approximation for a singular system

Cites Work

• Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds
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• Global heat kernel estimates
• Regularization methods for delta-function potential in two-dimensional quantum mechanics
• Regularization and renormalization in scattering from Dirac delta potentials
• Finitely many Dirac-delta interactions on Riemannian manifolds
• Nonrelativistic Lee model in three dimensional Riemannian manifolds
• DIFFUSION PROCESSES AND RIEMANNIAN GEOMETRY
• A correction to: Sobolev and isoperimetric inequalities for riemannian submanifolds
• Eigenvalue estimate on complete noncompact Riemannian manifolds and applications
• Renormalization in non-relativistic quantum mechanics
• Green’s-function approach to two- and three-dimensional delta-function potentials and application to the spin-1/2 Aharonov–Bohm problem
• The relativistic Lee model on Riemannian manifolds
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