Infrared and collinear divergences in gauge theories

L.V. Prokhorov
V.A. Fock Institute of Physics, St. Petersburg State University, ul. Ulyanovskaya 1, Petrodvorets, St. Petersburg, 198904, Russian Federation

The problem of infrared and collinear divergences is considered within the framework of perturbation theory and the scattering operator redefinition method. IR divergent processes in electrodynamics and gravitation (perturbation theory) are described, and for the case of electrodynamics a scattering operator free from IR divergences is constructed. For the massless electrodynamics model, a recipe for constructing a scattering operator free from both IR and collinear divergences is given. The meaning of experimental parameters entering the final formulas is discussed, and it is shown that the S-matrix factorization (i.e., the approximate independence of hard and soft processes) makes the theorem on the cancellation of divergences in observables trivial. A method for finding divergences in theories with multiparticle vertices is presented.

PACS: 11.10.−z, 11.15.−q (all)
DOI: 10.1070/PU1999v042n11ABEH000488
URL: https://ufn.ru/en/articles/1999/11/b/
Web of Science

000084282400002
Citation: Prokhorov L V "Infrared and collinear divergences in gauge theories" Phys. Usp. 42 1099–1120 (1999)

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Оригинал: Прохоров Л В «Инфракрасные и коллинеарные расходимости в калибровочных теориях» УФН 169 1199–1221 (1999); DOI: 10.3367/UFNr.0169.199911b.1199

References (82) Cited by (3) Similar articles (20) ↓

L.V. Prokhorov, S.V. Shabanov “Phase space of mechanical systems with a gauge group” Sov. Phys. Usp. 34 (2) 108–140 (1991)
V.B. Berestetskii “The dynamical properties of elementary particles and the theory” Sov. Phys. Usp. 5 7–36 (1962)
M.A. Shifman “Anomalies and low-energy theorems of quantum chromodynamics” Sov. Phys. Usp. 32 289–309 (1989)
V.A. Matveev, V.A. Rubakov et al “Nonconservation of baryon number under extremal conditions” Sov. Phys. Usp. 31 916–939 (1988)
B.L. Ioffe “Weak interactions at short distances” Sov. Phys. Usp. 16 459–484 (1974)
K.L. Zarembo, Yu.M. Makeenko “An introduction to matrix superstring models” Phys. Usp. 41 1–23 (1998)
A.V. Borisov, A.S. Vshivtsev et al “Photons and leptons in external fields at finite temperature and density” Phys. Usp. 40 229–255 (1997)
K.G. Selivanov “Counting vacua in supersymmetric Yang-Mills theory” Phys. Usp. 45 675–686 (2002)
A.V. Marshakov “String theory or field theory?” Phys. Usp. 45 915–954 (2002)
I.V. Andreev “Chromodynamics as a theory of the strong interaction” Sov. Phys. Usp. 29 971–979 (1986)
A.G. Polnarev, M.Yu. Khlopov “Cosmology, primordial black holes, and supermassive particles” Sov. Phys. Usp. 28 213–232 (1985)
M.A. Ol’shanetskii “A short guide to modern geometry for physicists” Sov. Phys. Usp. 25 123–129 (1982)
A.I. Vainshtein, V.I. Zakharov et al “ABC of instantons” Sov. Phys. Usp. 25 195–215 (1982)
A.A. Grib, E.V. Damaskinskii, V.M. Maksimov “The problem of symmetry breaking and in variance of the vacuum in quantum field theory” Sov. Phys. Usp. 13 798–815 (1971)
D.I. Blokhintsev “High-energy physics and the fundamental principles of modern theory” Sov. Phys. Usp. 8 612–613 (1966)
D.S. Kuz’menko, Yu.A. Simonov, V.I. Shevchenko “Vacuum, confinement, and QCD strings in the vacuum correlator method” Phys. Usp. 47 1–15 (2004)
L.B. Okun’ “Contemporary status and prospects of high-energy physics” Sov. Phys. Usp. 24 341–365 (1981)
E.L. Feinberg “On multiple production in collisions of ultra-high energy particles” Sov. Phys. Usp. 3 147–158 (1960)
V.S. Vikhrenko “Theory of depolarized molecular light scattering” Sov. Phys. Usp. 17 558–576 (1975)
I.M. Suslov “Development of a (4-ε)-dimensional theory for the density of states of a disordered system near the Anderson transition” Phys. Usp. 41 441–467 (1998)

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