Renormalization: Theories and Applications  

In General > s.a. [renormalization]; lattice field theory; quantum systems; regge calculus [general relativity].
@ Hamiltonian field theory: Maslov & Shvedov ht/98-in.
> Applications: see brownian motion; chaos; phase transitions.

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

–1() = –1(MX) + (b/2) log(MX / ) ;

this presents the Landau Pole problem; One finds that (E = 0) 1/137, and (E = 91 GeV = MZ) 1/128.
@ References: Feynman PR(48), PR(48); Tomonaga PR(48); Schwinger PR(48), PR(49); Dyson PR(49); 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.

Gauge Theories > s.a. electroweak; QCD; quantum gauge theories; topological field theories.
@ General references: 't Hooft NPB(71) [spontaneously broken, massive]; 't Hooft & Veltman NPB(72); Balaban CMP(84), CMP(88) [lattice]; Grigore ht/99, ht/00, JPA(04) [causal approach]; Fischer & Gies JHEP(04)hp [propagators]; Duetsch & Fredenhagen ht/04-in [BRST formalism]; 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 a0706-PhD [differential renormalization].
@ Gauge-invariant: Morris JHEP(00)ht, IJMPA(01)ht-in; Rosten ht/05-PhD, 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-in [SU(N)]; > s.a. yang-mills theories.
@ Higher-dimensional: Gies PRD(03)ht; Álvarez & Faedo JHEP(06)ht [6D QED].
@ Standard model: Hossenfelder PRD(04)hp [running constants and minimal length]; Actis et al NPB(07) [2-loop].
@ Supersymmetric: Piguet ht/96; Weinberg PRL(98)ht [non-renormalization theorem]; Stelle ht/02-in [sugra and super-Yang-Mills]; Berenstein & Rey PRD(03) [N = 2]; Guralnik et al ht/04-in [N = 2 and 4 super-Yang-Mills, non-renormalization theorems]; > s.a. specific theories.

Other Theories > s.a. boundaries; quantum field theory in curved spacetime.
@ Scalar fields: Bouzas IJMPA(03) [many scalars + fermions]; de Albuquerque ht/05 [4 with Robin boundary conditions]; Stevenson NPB(05) [vs lattice Ising model]; Gallavotti mp/05 [2D and 3D non-perturbative UV stability]; Sonoda ht/05-in [in E3]; de Aragão & Carneiro PLA(06) [4, by scaling]; Casadio a0806 [gravitational renormalization].
@ Scalar fields, curved spacetime: Bonanno PRD(95)gq [Einstein universe]; Hollands & Wald CMP(03)gq/02 [Klein-Gordon]; Kopper & Müller CMP(07) [4 on Riemanian manifolds].
@ Statistical mechanics: Fisher RMP(98) [scaling]; > s.a. critical phenomena.
@ Gravity: Fukuma & Matsuura PTP(02) [classical higher-derivative]; Anselmi JHEP(07)ht/06 [semiclassical]; > s.a. renormalization of quantum gravity and covariant quantum gravity.
@ Non-renormalizable: Barvinsky et al PRD(93)gq; Gegelia et al ht/95; Gomis & Weinberg NPB(96)ht/95; Blasi et al PRD(99) [mapped to renormalizable ones]; Japaridze & Gegelia IJTP(00) [perturbative approach]; Klauder LMP(03)ht/02 [4n theories, n 4], JSP(04)ht/03 [p3, p = 8, 10, 12, ...]; Anselmi JHEP(05)ht [class including all self-interacting scalars]; Kazakov & Vartanov ht/06 [renormalizable expansions]; Klauder AP(07)ht/06 [new approach]; Klauder a0805 [divergence-free].
@ Quantum mechanics: Manuel & Tarrach PLB(94); Polonyi AP(96); Gosselin & Mohrbach JPA(00); Birse a0709-in [non-relativistic scattering].
@ Cosmology: Iguchi et al PRD(98); Ibáñez & Jhingan IJTP(07)gq; Woodard a0805 [cosmology is not a renormalization group flow]; > s.a. cosmological models.
@ Models: Kraus & Griffiths AJP(92); Bresser et al ht/99 [Lorentz-invariant renormalization]; Pernici et al NPB(00) [Yukawa theories, dimensional].
> Related topics: see Coarse Structures in Geometry; path integrals; quantum field theory; renormalization group; sigma model.

Non-Standard Theories > s.a. Disorder.
@ Discrete models: Dorogovtsev PRE(03)cm [evolving networks]; Requardt JMP(03) [discrete quantum spacetime], mp/03 [many-body, critical regime]; > s.a. hilbert space, regge calculus.
@ Non-commutative: Gayral et al PLB(05)ht/04 [possible trouble]; Rivasseau et al CMP(06)ht/05 [4]; Grosse & Steinacker NPB(06)ht/05 [3], ht/06 [6D 3]; Grosse & Wohlgenannt ht/06-in; Vignes-Tourneret mp/06-PhD; Rivasseau & Vignes-Tourneret ht/07-in; Rivasseau & Vignes-Tourneret ht/07-in; Rivasseau a0705 [rev]; Gurau & Tanasa a0706 [and dimensional regularization]; Tanasa & Vignes-Tourneret a0707 [Hopf algebra structure]; Razvan a0711-in [4*4]; Gurau a0802-PhD.
@ Other theories: Bezerra et al PRD(04) [deformed]; Anselmi & Halat PRD(07) [Lorentz-violating].


Main pageAbbreviationsJournalsCommentsOther sitesAcknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified 19 jul 2008