Renormalization of Gauge Theories| 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.
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