# 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.

## 27 Citations

Boundary Conditions that Remove Certain Ultraviolet Divergences

- PhysicsSymmetry
- 2021

A novel way of removing UV divergences is reviewed: by imposing a type of boundary condition on the wave function that allows for a direct definition of the Hamiltonian without renormalization or limiting procedures.

On Nelson-Type Hamiltonians and Abstract Boundary Conditions

- PhysicsCommunications in Mathematical Physics
- 2019

We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation…

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

- Physics, Mathematics
- 2017

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the…

Hamiltonians without ultraviolet divergence for quantum field theories

- PhysicsQuantum Studies: Mathematics and Foundations
- 2020

We propose a way of defining Hamiltonians for quantum field theories without any renormalization procedure. The resulting Hamiltonians, called IBC Hamiltonians, are mathematically well defined (and…

New Type of Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories

- Mathematics
- 2015

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…

Interior-boundary conditions for many-body Dirac operators and codimension-1 boundaries

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

We are dealing with boundary conditions for Dirac-type operators, i.e. first order differential operators with matrix-valued coefficients, including in particular physical many-body Dirac operators.…

Particle creation and annihilation at interior boundaries: one-dimensional models

- Mathematics
- 2015

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,…

The Massless Nelson Hamiltonian and Its Domain

- PhysicsSpringer INdAM Series
- 2020

In the theory of point interactions, one is given a formal expression for a quantum mechanical Hamiltonian. The interaction terms of the Hamiltonian are singular: they can not be rigorously defined…

An abstract framework for interior-boundary conditions

- Mathematics
- 2021

In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally,…

Interior-boundary conditions for Schrödinger operators on codimension-1 boundaries

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

Interior-boundary conditions (IBCs) are boundary conditions on wave functions for Schrödinger equations that allow that probability can flow into (and thus be lost at) a boundary of configuration…

## References

SHOWING 1-10 OF 25 REFERENCES

New Type of Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories

- Mathematics
- 2015

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

- Mathematics
- 2015

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

- Physics
- 1992

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

- PhysicsJournal of Statistical Physics
- 2019

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

- Physics
- 2003

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

- Physics
- 1954

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

- Physics, Mathematics
- 1964

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

- Mathematics
- 1984

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

- Mathematics
- 2009

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

- Physics, Mathematics
- 2003

Introduction.- First-order adiabatic theory.- Space-adiabatic perturbation theory.- Applications and extensions.- Quantum dynamics in periodic media.- Adiabatic decoupling without spectral gap.-…