nLab
ultraviolet divergence

Contemts

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contemts

Idea

In the construction of quantum field theory various naive mathematical constructions give rise to ill-defined “divergent” expressions.

Some of these occur in the limit that interaction point are taken close to each other. Since the short distances involved in this limit translates, under Fourier transform, to high frequencies enoded in the wave front set of the distributions; these are called ultraviolet divergences. The correct way to deal with them is called renormalization.

Other divergences occcur in the limit that the spactime support of the interaction (the support of the “adiabatic switching”) tends without bounds to all of spacetime, also called the adiabatic limit. Since this large distance involved in this limit translate, under Fourier transform to low frequencies, these are called infrared divergences.

References

See also

Last revised on November 6, 2017 at 07:20:52. See the history of this page for a list of all contributions to it.