Infrared problem in perturbative quantum field theory

  title={Infrared problem in perturbative quantum field theory},
  author={Paweł Duch},
  journal={Reviews in Mathematical Physics},
  • Paweł Duch
  • Published 3 June 2019
  • Physics, Mathematics
  • Reviews in Mathematical Physics
We propose a mathematically rigorous construction of the scattering matrix and the interacting fields in models of relativistic perturbative quantum field theory with massless fields and long-range interactions. We consider quantum electrodynamics and a certain model of interacting scalar fields in which the standard definition of the scattering matrix is not applicable because of the infrared problem. We modify the Bogoliubov construction using the ideas of Dollard, Kulish and Faddeev. Our… Expand

Figures from this paper

Infraparticle quantum fields and the formation of photon clouds
A non-perturbative and exactly solvable quantum field theoretical model for a “dressed Dirac field” is presented, that exhibits all the kinematical features of QED: an appropriate delocalization ofExpand
Almost radial gauge
An almost radial gauge A of the electromagnetic potential is constructed for which x ̈ Apxq vanishes arbitrarily fast in timelike directions. This potential is in the class introduced by Dirac withExpand
Infrared Problem vs Gauge Choice: Scattering of Classical Dirac Field
We consider the Dirac equation for the classical spinor field placed in an external, time-dependent electromagnetic field of the form typical for scattering settings:Expand


Infrared problems in quantum electrodynamics
We present a self-contained treatment of the infrared problem in Quantum Electrodynamics. Our program includes a derivation and proof of finiteness of modified reduction formulae for scattering inExpand
Massless fields and adiabatic limit in quantum field theory
The thesis is devoted to a rigorous construction of the Wightman and Green functions in models of the perturbative quantum field theory in the four-dimensional Minkowski spacetime in the framework ofExpand
Charges from Dressed Matter: Physics and Renormalisation
Abstract Gauge theories are characterised by long range interactions. Neglecting these interactions at large times and identifying the Lagrangian matter fields with the asymptotic physical fieldsExpand
The Infrared Problem in QED: A Lesson from a Model with Coulomb Interaction and Realistic Photon Emission
The scattering of photons and heavy classical Coulomb interacting particles, with realistic particle–photon interaction (without particle recoil) is studied adopting the Koopman formulation for theExpand
Weak Adiabatic Limit in Quantum Field Theories with Massless Particles
We construct the Wightman and Green functions in a large class of models of perturbative QFT in the four-dimensional Minkowski space in the Epstein–Glaser framework. To this end we prove theExpand
Microlocal Analysis and¶Interacting Quantum Field Theories:¶Renormalization on Physical Backgrounds
Abstract:We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) space-times. We develop a purely local version of theExpand
The infrared divergence phenomena and high-energy processes
Abstract A general treatment of the infrared divergence problem in quantum electrodynamics is given. The main feature of this treatment is the separation of the infrared divergences as multiplicativeExpand
A Local (Perturbative) Construction of Observables in Gauge Theories: The Example of QED
Abstract:Interacting fields can be constructed as formal power series in the framework of causal perturbation theory. The local field algebra is obtained without performing the adiabatic limit; theExpand
Asymptotic symmetries of QED and Weinberg’s soft photon theorem
A bstractVarious equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gaugeExpand
Large gauge symmetries and asymptotic states in QED
A bstractLarge Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity.Expand