Avoiding Ultraviolet Divergence by Means of Interior–Boundary Conditions

@article{Teufel2016AvoidingUD,
  title={Avoiding Ultraviolet Divergence by Means of Interior–Boundary Conditions},
  author={Stefan Teufel and Roderich Tumulka},
  journal={arXiv: Quantum Physics},
  year={2016},
  pages={293-311}
}
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. 
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  • R. Tumulka
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  • 2020
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References

SHOWING 1-10 OF 25 REFERENCES
New Type of Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
We propose a novel type of Hamiltonians for quantum eld theories. They are mathematically well-dened (and in particular, ultraviolet nite) without any ultraviolet cut-o such as smearing out the
Particle creation and annihilation at interior boundaries: One-dimensional models
We describe creation and annihilation of particles at external sources in one spatial dimension in terms of interior-boundary conditions (IBCs). We derive explicit solutions for spectra,
On a zero-range interaction of a quantum particle with the vacuum
Self-adjoint extensions of the operator- Delta with the domain C0infinity (R3) in the space Ck(+)L2(R3) are described. Such operators are interpreted as Hamiltonians of a point interaction of a
Bohmian Trajectories for Hamiltonians with Interior–Boundary Conditions
Recently, there has been progress in developing interior–boundary conditions (IBCs) as a technique of avoiding the problem of ultraviolet divergence in non-relativistic quantum field theories while
Van Hove Hamiltonians – Exactly Solvable Models of the Infrared and Ultraviolet Problem
Abstract. Quadratic bosonic Hamiltonians with a linear perturbation are studied. Depending on the infrared and ultraviolet behavior of the perturbation, their properties are described from the point
Some Special Examples in Renormalizable Field Theory
Some special problems of interacting fields that contain removable divergences are treated in detail. Comparisons with the power series renormalization procedures are made. Examination of the closed
Interaction of Nonrelativistic Particles with a Quantized Scalar Field
We demonstrate the mathematical existence of a meson theory with nonrelativistic nucleons. A system of Schrodinger particles is coupled to a quantized relativistic scalar field. If a cutoff is put on
Multiparticle Schrödinger Hamiltonians with point interactions
We construct the resolvent for a nonrelativistic multiparticle Schroedinger Hamiltonian having point interactions, and accommodating annihilation and creation of, at most, three particles. The
Time Evolution of the External Field Problem in QED
We construct the time-evolution for the second quantized Dirac equation subject to a smooth, compactly supported, time dependent electromagnetic potential and identify the degrees of freedom
Adiabatic perturbation theory in quantum dynamics
Introduction.- First-order adiabatic theory.- Space-adiabatic perturbation theory.- Applications and extensions.- Quantum dynamics in periodic media.- Adiabatic decoupling without spectral gap.-
...
...