Renormalization of Gauge Theories  

In General > s.a. history of particle physics; lattice gauge theories; quantum gauge theories.
* Coupling constants: Robinson & Wilczek have calculated the contribution of graviton exchange to the running of gauge couplings at lowest non-trivial order in perturbation theory; The results indicate that the gravitational correction renders all gauge couplings asymptotically free.
@ General references: 't Hooft NPB(71) [spontaneously broken, massive]; 't Hooft & Veltman NPB(72); Balaban CMP(84), CMP(88) [lattice]; Grigore ht/99, JPA(00), ht/00, JPA(04) [Epstein-Glaser, causal approach]; Fischer & Gies JHEP(04)hp [propagators]; Faddeev TMP(06) [charge and dimensional transmutation]; van Suijlekom CMP(07)ht/06, a0801-in [Hopf algebra approach]; Tomboulis & Velytsky PRL(07) [Monte-Carlo-improved action]; Seijas PhD(07)-a0706 [differential renormalization]; Tomboulis MPLA(09) [free energies and order parameters]; Faddeev IJMPA(16)-a1509-conf; Romatschke a1910 [3D, beta function].
@ BRST formalism: Duetsch & Fredenhagen ht/04-en; Asnafi et al a1811 [BRS- invariant RG flows].
@ Yang-Mills theory: 't Hooft NPB(71) [massless]; Bochicchio a1701 [large-N limit, ultraviolet finiteness].
@ Gravitational corrections to coupling constants: Robinson & Wilczek PRL(06); Toms IJMPD(08); Robinson & Wilczek PRL(10) + news ns(10)nov; Folkerts et al PLB(12)-a1101 [no contribution]; Ellis & Mavromatos PLB(12); Felipe et al MPLA(13)-a1206 [for QED, ambiguities]; > s.a. renormalization [coupling constants].
@ Gauge-invariant: Morris JHEP(00)ht, IJMPA(01)ht-conf; Rosten PhD(05)ht, IJMPA(06) [manifestly]; Morris & Rosten PRD(06)ht/05 [2-loop beta function]; Arnone et al EPJC(07)ht/05 [generalized]; Arnone et al ht/06-proc [SU(N)]; > s.a. yang-mills theories.
@ In curved spacetime: Lavrov & Shapiro PRD(10)-a0911 [gauge- and diffeomorphism-invariant].

Maxwell Theory, QED > s.a. fine-structure constant; Hopf Algebra; QED variations; vacuum.
* Coupling constant: For α = e2/\(\hbar\)c, in general, to one-loop level,

α−1(μ) = α−1(MX) + (b/2π) log(MX / μ) ;

this presents the Landau Pole problem; One finds that α(E = 0) ≅ 1/137, and α(E = 91 GeV = MZ) ≅ 1/128.
@ Early papers: Feynman PR(48), PR(48); Tomonaga PR(48); Schwinger PR(48), PR(49); Dyson PR(49).
@ General references: Su et al JPG(99)ht/05 [mass-dependent subtraction]; Gies & Jaeckel PRL(04)hp; Prokhorenko & Volovich PSIM(04)ht/06 [Hopf algebra approach]; Fujita ht/06; Suslov a0911-conf [beta-function, strong-coupling asymptotics]; Ardalan et al PS(13)-a1108 [gauge-invariant cutoff]; Kolomeisky a1309 [optimal number of terms]; Masood PRI(14)-a1407 [near decoupling temperatures]; Jora & Schechter a1407 [new, semi-perturbative renormalization scheme]; Dimock a1712 [3D, ultraviolet stability]; Gies & Ziebell a2005 [asymptotic safety].
@ Lorentz-violating quantum electrodynamics: Anselmi & Taiuti PRD(10)-a0912; Santos & Sobreiro BJP(16)-a1502 [and CPT-violating].

Other Types of Theories and Generalizations > s.a. electroweak theory; topological field theories.
* QCD: The theory is renormalizable in 4D, superrenormalizable in lower dimensions; The large-N S-matrix is only renormalizable, not UV finite.
@ QCD: Wilson PRD(71); Kadanoff RMP(77); Peng PLB(06) [coupling constant];
Morris & Rosten JPA(06)ht [gauge-invariant]; Andrasi & Taylor AP(09)-a0704 [Hamiltonian, Coulomb gauge]; Fried et al AP(15)-a1412 [finite, non-perturbative]; Bochicchio a1701 [large-N limit]; > s.a. QCD [asymptotic freedom]; QCD phenomenology [confinement].
@ QCD, running coupling constant: Shirkov & Solovtsov PRL(97) [analytic model]; Gaddah ht/02 [and observables]; Fritzsch MPLA(06) [t-dependence of QCD scale].
@ Standard model: Hossenfelder PRD(04)hp [running constants and minimal length]; Actis et al NPB(07) [2-loop]; Haba et a NPB(14) [neutrino sector].
@ Higher-dimensional: Gies PRD(03)ht; Álvarez & Faedo JHEP(06)ht [6D QED].
@ Supersymmetric: Piguet ht/96; Weinberg PRL(98)ht [non-renormalization theorem]; Stelle AIP(01)ht/02 [supergravity and super-Yang-Mills]; Berenstein & Rey PRD(03) [N = 2]; Guralnik et al IJMPA(05)ht/04-conf [N = 2 and 4 super-Yang-Mills, non-renormalization theorems]; Cherchiglia et al EPJC(16)-a1508 [calculation of the beta function]; > s.a. specific theories.
@ Non-commutative theories: Blaschke et al FdP(10)-a0908 [review, problem]; van Suijlekom CMP(12)-a1104 [Yang-Mills spectral action].
@ Other types: Shi & Shrock PRD(15)-a1411 [chiral gauge theories]; Junqueira et al a1807 [topological Yang-Mills theories]; > s.a. other theories.

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 22 may 2020