Infrared problem in perturbative quantum field theory

@article{Duch2021InfraredPI,
  title={Infrared problem in perturbative quantum field theory},
  author={Paweł Duch},
  journal={Reviews in Mathematical Physics},
  year={2021}
}
  • Paweł Duch
  • Published 3 June 2019
  • Physics
  • 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… 
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A Correction to this paper has been published: https://doi.org/10.1007/s00023-020-01015-y

References

SHOWING 1-10 OF 112 REFERENCES
Infrared problems in quantum electrodynamics
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 of…
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 fields…
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 the…
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 the…
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 the…
The infrared divergence phenomena and high-energy processes
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; the…
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 gauge…
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.…
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