# Hamiltonians without ultraviolet divergence for quantum field theories

@article{Teufel2020HamiltoniansWU, title={Hamiltonians without ultraviolet divergence for quantum field theories}, author={Stefan Teufel and Roderich Tumulka}, journal={Quantum Studies: Mathematics and Foundations}, year={2020}, volume={8}, pages={17-35} }

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 in particular, ultraviolet finite) without an ultraviolet cutoff such as smearing out the particles over a nonzero radius; rather, the particles are assigned radius zero. These Hamiltonians agree with those obtained through renormalization whenever both are known to exist. We describe explicit…

## 11 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.

Quantum field theory without divergence: the method of the interaction operators

- Physics
- 2016

The recently proposed interior boundary conditions approach [S. Teufel and R. Tumulka: Avoiding Ultraviolet Divergence by Means of Interior Boundary Conditions, arXiv:1506.00497] is a method for…

The Nelson Model on Static Spacetimes

- Physics
- 2021

The Nelson model describes the interaction of nonrelativistic quantum particles with a relativistic quantum field of scalar bosons. Nelson rigorously demonstrated in 1964 the existence of a…

Consistency Proof for Multi-time Schrödinger Equations with Particle Creation and Ultraviolet Cut-Off

- Mathematics
- 2020

For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schrodinger equation consists of several…

Consistency of multi-time Dirac equations with general interaction potentials

- Mathematics
- 2016

In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for…

Ultraviolet Renormalisation of a quantum field toy model I

- Physics
- 2021

We consider a class of Hamiltonians describing a fermion field coupled to a boson field. The interaction kernels are assumed bounded in the fermionic momentum variable and decaying like |q| for large…

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,…

A Lorentz-covariant interacting electron–photon system in one space dimension

- Physics
- 2019

A Lorenz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is…

On semi-relativistic quantum mechanics of $N$-body systems composed of nuclei, electrons, and photons

- Physics
- 2020

A quantum-mechanical model is developed which reproduces the atomic and molecular energy spectra of the many-body Pauli equation with Coulomb interactions and external electro- and magneto-static…

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,…

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