Avoiding Ultraviolet Divergence by Means of Interior-Boundary Conditions

Abstract

We describe here a novel way of defining Hamiltonians for quantum field theories (QFTs), based on the particle-position representation of the state vector and involving a condition on the state vector that we call an "interior-boundary condition." At least for some QFTs (and, we hope, for many), this approach leads to a well-defined, self-adjoint Hamiltonian without the need for an ultraviolet cut-off or renormalization.

18 pages LaTeX, 2 figures; presentation given at the conference "Quantum Mathematical Physics" in Regensburg (Germany), Sept. 29-Oct. 2, 2014 (http://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/qft2014/index.html)

References in corpus (4)

• Photon wave function
• Multi-Time Wave Functions for Quantum Field Theory
• Particle creation and annihilation at interior boundaries: One-dimensional models
• Fermionic Wave Functions on Unordered Configurations

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• Multi-Time Wave Functions
• Interior-Boundary Conditions for Many-Body Dirac Operators and Codimension-1 Boundaries
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• The resolvent of the Nelson Hamiltonian improves positivity
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• Multi-Time Version of the Landau-Peierls Formulation of Quantum Electrodynamics
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