Hamiltonians without ultraviolet divergence for quantum field theories

  title={Hamiltonians without ultraviolet divergence for quantum field theories},
  author={Stefan Teufel and Roderich Tumulka},
  journal={Quantum Studies: Mathematics and Foundations},
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… 

Boundary Conditions that Remove Certain Ultraviolet Divergences

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.

The Nelson Model on Static Spacetimes

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

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

Ultraviolet Renormalisation of a quantum field toy model I

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

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

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

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

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,

Semi-relativistic $N$-body quantum mechanics of electrons and photons, with fixed nuclei

It is argued that by the end of the 1920s a quantum-mechanical model could have been in place, that not only produces the atomic and molecular energy levels of the many-body Pauli equation with



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

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

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

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

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.

On a direct description of pseudorelativistic Nelson Hamiltonians

Abstract interior-boundary conditions (IBC's) allow for the direct description of the domain and the action of Hamiltonians for a certain class of ultraviolet-divergent models in Quantum Field

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

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

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

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

Fermionic Wave Functions on Unordered Configurations

Quantum mechanical wave functions of N identical fermions are usually represented as anti-symmetric functions of ordered configurations. Leinaas and Myrheim proposed how a fermionic wave function can

Relativistic interactions by means of boundary conditions: The Breit–Wigner formula

The relativistic generalization of the Breit–Wigner formula presented in this paper is not based on perturbative quantum field theory. Rather, it starts with two free Klein–Gordon or Dirac particles

Avoiding Ultraviolet Divergence by Means of Interior–Boundary Conditions

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

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