Renormalization:
Theories and Applications| Renormalization:
Theories and Applications |
In General > s.a. [renormalization]; lattice
field theory; quantum systems; regge
calculus [general relativity].
@ Types of theories: Maslov & Shvedov ht/98-in
[Hamiltonian field theories]; Chen & Huang a0904 [theories
at a Lifshitz point, UV behavior].
> Applications: see brownian
motion; chaos; phase
transitions.
Maxwell Theory, QED > s.a. fine-structure
constant; Hopf Algebra; QED
variations; vacuum.
* 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;
Suslov a0911-in
[beta-function, strong-coupling asymptotics].
Gauge Theories > s.a. electroweak
theory; QCD; quantum
gauge theories; topological
field theories.
@ General references: 't Hooft NPB(71)
[Yang-Mills, massless], 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];
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]; > s.a. renormalization [coupling
constants].
@ 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
[supergravity
and
super-Yang-Mills];
Berenstein & Rey PRD(03)
[N = 2]; Guralnik et al IJMPA(05)ht/04-in
[N = 2 and 4 super-Yang-Mills, non-renormalization theorems]; > s.a. specific
theories.
Other Theories > s.a. covariant
quantum gravity; quantum
gravity renormalization; quantum
field theory in curved spacetime; stress-energy
tensor.
@ Scalar fields: Bouzas
IJMPA(03)
[many scalars + fermions]; Stevenson NPB(05)
[vs lattice Ising model]; Gallavotti in(06)mp/05 [2D
and 3D
non-perturbative UV stability]; Sonoda ht/05-in
[in
E3]; Casadio a0806 [gravitational
renormalization].
@ Scalar fields, 
4:
Pinter AdP(01)
[Epstein-Glaser
approach]; de Albuquerque ht/05 [with
Robin boundary conditions]; de Aragão & Carneiro PLA(06)
[by
scaling]; Suslov a0911-in
[beta-function, strong-coupling asymptotics].
@ 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.
@ 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 JPA(06), ht/06 [renormalizable
expansions]; Klauder AP(07)ht/06 [new
approach]; Klauder JPA(08)-a0805 [divergence-free],
JPA-a0811, a0904-in
[approach]; Sonoda a0909 [continuum limit].
@ 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 PRL(08)-a0805 [cosmology
is not a renormalization-group flow]; > s.a. cosmological
models.
@ Models: Kraus & Griffiths AJP(92)nov;
Bresser
et
al ht/99 [Lorentz-invariant
renormalization]; Pernici et al NPB(00)
[Yukawa theories, dimensional]; Yang JPA(09)-a0901 [effective
theories, non-perturbative
renormalization].
> Related topics: see boundaries; 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]; Gittsovich et al a0908/NJP
[2D random-field Ising model]; > s.a. hilbert
space, networks, 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],
ATMP-ht/06 [6D 3];
Grosse & Wohlgenannt JPCS(07)ht/06;
Vignes-Tourneret mp/06-PhD;
Rivasseau & Vignes-Tourneret ht/07-in;
Rivasseau & Vignes-Tourneret ht/07-in;
Rivasseau a0705 [rev];
Gurau & Tanasa AHP(08)-a0706 [and
dimensional regularization]; Tanasa & Vignes-Tourneret a0707 [Hopf
algebra structure]; Razvan a0711-in
[4*4];
Gurau a0802-PhD;
Blaschke a0908 [problem with gauge theories, review].
@ Other types of theories: Bezerra et al PRD(04)
[deformed]; Anselmi & Halat PRD(07)
[Lorentz-violating]; López & Mazzitelli PLB(09)-a0810 [with
modified dispersion relations]; Iengo et al a0906 [Lifshitz-type theories].
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nov 2009