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

@article{Tumulka2020InteriorboundaryCF, title={Interior-boundary conditions for Schr{\"o}dinger operators on codimension-1 boundaries}, author={Roderich Tumulka}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2020}, volume={53} }

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 space while getting added in another part of configuration space. IBCs are of particular interest because they allow for defining Hamiltonians involving particle creation and annihilation (as used in quantum field theories) without the need for renormalization or ultraviolet cut-off. For those…

## 10 Citations

Interior-Boundary Conditions for the Dirac Equation at Point Sources in 3 Dimensions

- Mathematics
- 2020

A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the…

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.

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…

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,…

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…

Hamiltonians for polaron models with subcritical ultraviolet singularities

- Physics
- 2022

We treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity,…

Multi-time formulation of particle creation and annihilation via interior-boundary conditions

- MathematicsReviews in Mathematical Physics
- 2019

Interior-boundary conditions (IBCs) have been suggested as a possibility to circumvent the problem of ultraviolet divergences in quantum field theories. In the IBC approach, particle creation and…

Complex charges, time reversal asymmetry, and interior-boundary conditions in quantum field theory

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2019

While fundamental physically realistic Hamiltonians should be invariant under time reversal, time asymmetric Hamiltonians can occur as mathematical possibilities or effective Hamiltonians. Here, we…

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.…

Bohmian mechanics at space–time singularities. I. Timelike singularities

- Physics, MathematicsJournal of Geometry and Physics
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Interior-boundary conditions (IBCs) have been suggested as a possibility to circumvent the problem of ultraviolet divergences in quantum field theories. In the IBC approach, particle creation and…

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