Renormalization Group| Renormalization Group |
In General
> s.a. renormalization / for applications, see specific
types of theories and quantum gravity.
* History: The
technique was developed in 1973 by Ken Wilson.
* Idea: A group of
transformations on the (renormalized) parameters of a theory (mass,
wave function, coupling constants) corresponding to changes of the
renormalization conditions (subtraction point), under which the
physics is required to be invariant.
* Applications: The
invariance requirement provides non-trivial constraints on the asymptotic
behavior of the theory; Renormalization group ideas are largely
responsible for the considerable success achieved in developing a
quantitative theory of phase transitions.
> Applications: see
Disordered Systems; phase transitions;
random walk; statistics.
Renormalization Group Equation
> s.a. chaos [period-doubling bifurcation].
* Idea: It expresses
the connection between scale transformations and renormalizability
of a theory; Like a mathematical microscope, it allows us to look
at very-small-scale physics from the behavior at larger scales.
* Callan-Symanzik equation:
An analytic form of the renormalization group invariance; For
λφ4 theory, it is
(μ ∂/∂μ + β ∂/∂λ − nγ) ΓR(n)(pi; λ, μ) = −i μ2 α Γφ^2 R(n)(0, pi; λ, μ) .
* Beta function: (or Gell-Mann-Low function).
@ General references:
Callan PRD(70);
Symanzik CMP(70);
Curtright & Zachos PRD(11)-a1010 [global structure of group trajectories].
@ Geometric view:
Dolan IJMPA(95),
IJMPA(95),
IJMPA(97);
Jackson et al a1312
[for holographic theories].
@ Functional renormalization group: Polonyi CEJP(03)ht/01-ln;
Pawlowski AP(07)ht/05;
Weyrauch JPA(06) [and tunneling];
Benedetti et al JHEP(11)-a1012;
Vacca & Zambelli PRD(11)-a1103 [regularization and coarse-graining in phase space];
Metzner et al RMP(12) [and correlated fermion systems];
Nagy AP(14)-a1211-ln [intro, and asymptotic safety];
Codello et al PRD(14)-a1310 [scheme dependence and universality];
Mati PRD(15)-a1501 [Vanishing Beta Function curves];
Codello et al PRD(15)-a1502 [and local renormalization group],
EPJC(16)-a1505 [and effective action];
de Alwis JHEP(18)-a1707 [and quantum gravity].
@ Related topics: Simionato IJMPA(00)ht/98,
IJMPA(00)ht/98,
IJMPA(00) [and gauge symmetry];
Gosselin et al PLA(99)qp/00,
Gosselin & Mohrbach JPA(00)qp/98 [1-particle quantum mechanics, finite T];
Litim & Pawlowski PRD(02) [perturbative expansion];
Baume et al JHEP(14)-a1401 [Callan-Symanzik equation];
Harst & Reuter AP(15)-a1410 [new, simpler to use functional flow equation].
References
> s.a. Emergence; higgs mechanism;
types of metrics [information geometry].
@ Textbooks, reviews: Coleman in(71);
Wilson & Kogut PRP(74);
Wallace & Zia RPP(78);
in Cheng & Li 84;
Shirkov IJMPA(88),
IJMPB(98)ht/97;
Binney et al 92;
Goldenfeld 93;
Benfatto & Gallavotti 95;
Intriligator hp/98-proc;
Mironov & Morozov PLB(00);
O'Connor & Stephens ed-PRP(01);
Rivero ht/02-ln;
Amit & Martín-Mayor 05;
Mitter mp/05-en [mathematical];
Sonoda ht/06-ln [and perturbation theory];
Hollowood a0909-ln [and quantum field theory and supersymmetry];
Meurice et al PTRS(11)-a1102 [new applications];
Dimock RVMP(13)-a1108,
JMP(13)-a1212,
AHP(14)-a1304 [Balaban's approach];
Sfondrini a1210-ln [and universality];
Hollowood 13;
Bauerschmidt et al a1907-book.
@ Simple:
Maris & Kadanoff AJP(78)jun;
Wilson SA(79)aug;
Hans AJP(83)aug.
@ History:
Stückelberg & Peterman HPA(53) [discovery];
Shirkov & Kovalev PRP(01)mp/00-proc;
Peskin JSP(14)-a1405 [Ken Wilson and strong interactions].
@ Critical phenomena:
Fisher RMP(74);
Wilson RMP(75),
RMP(83);
Barber PRP(77) [intro];
Schmidhuber AJP(97)nov-ht;
Bhattacharjee cm/00-ln;
Pelissetto & Vicari PRP(02);
Requardt mp/02 [many-body systems];
Singh a1402
[and mean-field theory phase transitions, pedagogical];
Giuliani et al JHEP-a2008 [introduction and fermionic example];
> s.a. critical phenomena; phase transitions.
@ Non-perturbative: Phillips et al AP(98);
Aoki et al PTP(02)qp;
Berges et al PRP(02) [and statistical mechanics];
Blaizot et al PLB(06)ht/05 [solution],
PRE(06)ht/05,
PRE(05) [and p-dependence of n-point functions];
Delamotte cm/07 [intro];
Canet & Chaté JPA(07) [Model A, critical dynamics];
Pinson CMP(08);
Dupuis & Sengupta EPJB(08)-a0807 [for lattice models];
Balog et al a1907
[convergence of non-perturbative approximations];
Dupuis et al a2006 [rev];
> s.a. N-point functions.
@ Holographic: Balasubramanian & Kraus PRL(99) [and AdS];
Álvarez & Gómez PLB(00)ht;
de Boer FdP(01)ht-in;
Erdmenger PRD(01)ht;
Bianchi et al NPB(02)ht/01;
Skenderis CQG(02)ht-ln;
Fukuma et al PTP(03)ht/02 [rev];
Heemskerk & Polchinski JHEP(11)-a1010 [and Wilsonian RG];
Park & Mann JHEP(12) [asymptotically flat gravity].
@ UV fixed points: Gies & Janssen PRD(10)-a1006 [3D Thirring model];
Eichhorn et al EPJC(16)-a1510 [in multi-field models];
> s.a. asymptotic safety in quantum gravity.
@ IR fixed points: Ryttov & Shrock PRD(12)-a1206 [scheme transformations in the vicinity of an infrared fixed point];
> s.a. quantum-gravity renormalization.
@ Fixed points, other: Alexandre a0711 [misleading, free fixed point];
Berges & Wallisch PRD(17)-a1607 [non-thermal fixed points];
Jepsen & Popov a2105 [fixed points and homoclinic flows].
@ Without fixed points: Glazek & Wilson PRL(02)ht [limit cycles and chaos];
Rosten JHEP(09)-a0808 [from exact renormalization group];
Bulycheva & Gorsky a1402-fs [limit cycles].
@ Exact renormalization group: Sonoda JPA(07)ht/06 [vs ordinary];
Rosten PRP(12)-a1003 [fundamentals];
Baldazzi et al a2105 [practical computations].
@ And information theory: Apenko PhyA(12) [information loss and irreversibility of RG flow];
Bény & Osborne PRA(15)-a1206 [information-geometry approach];
Li LMP(17)-a1604 [irreversibility of the renormalization group flow and entropy];
DeBrota a1609.
@ And conformal symmetry: Komargodski & Schwimmer JHEP(11)-a1107 [4D renormalization group flows and spontaneously broken conformal symmetry];
Komargodski JHEP(12)-a1112;
Rosten a1806
[generalization to curved space, motivated by the conformal anomaly];
Giuliani a2012-talk [intro].
@ Related topics:
Wilson AiM(75);
Lässig NPB(90);
Minic & Nair IJMPA(96) [wave functionals and eigenvalues];
Jona-Lasinio PRP(01) [and probability theory];
Requardt cm/01 [scaling limit];
Dütsch & Fredenhagen ht/05-proc [in terms of algebraic quantum field theory];
RG2005 JPA(06);
Chishtie et al IJMPE(07)ht/06 [improvement];
Streets JGP(09) [singularity formation];
Yin CMP(11)-a0911 [spectral properties at infinite temperature];
Yin JMP(11)-a0911 [cluster-expansion approach];
Gaberdiel & Hohenegger JHEP(10) [supersymmetric flows];
Dütsch CM(12)-a1012-in
[connection between the Stückelberg-Petermann and Wilson renormalization groups];
Bény & Osborne NJP(15)-a1402 [and effectively indistinguishable microscopic theories];
Dias et al PLB(14)-a1407 [renormalization-group improved effective potential];
Altaisky PRD(16)-a1604 [and wavelets];
Bal et al PRL(17)-a1703 [using tensor networks];
Herren & Thomsen a2104 [ambiguities and divergences];
Yukalov PPN-a2105 [and approximation theory];
> s.a. diffusion.
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