Renormalization: Application and Specific Types of Theories |
In General
> s.a. renormalization / lattice field theory;
quantum systems; regge calculus [general relativity].
@ Statistical mechanics:
Fisher RMP(98) [scaling];
Tauber NPPS(12)-a1112 [intro];
Efrati et al RMP(14) [real space];
> s.a. critical phenomena.
@ Quantum mechanics:
Manuel & Tarrach PLB(94);
Polonyi AP(96);
Gosselin & Mohrbach JPA(00);
Birse a0709-conf [non-relativistic scattering];
Radičević a1608;
Paik a1707 [particle on a half-line].
@ 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.
@ Fermions: Jakovác et al EPJC(15)-a1406 [non-Gaussian fixed points];
> s.a. renormalization.
@ Many-body systems: Requardt mp/03 [critical regime];
Schwenk & Polonyi ed-12 [and effective field theory].
@ Discrete models: Dorogovtsev PRE(03)cm [evolving networks];
Requardt JMP(03) [discrete quantum spacetime];
Gittsovich et al NJP(10)-a0908 [2D random-field Ising model];
Yin JMP(11)-a1108 [Ising-type lattice spin systems];
Yin PhyA(13) [1D Ising model, Markov-chain approach];
Zinati & Codello JSM(18)-a1707 [Potts model];
> s.a. hilbert space; networks;
regge calculus; tensor networks.
@ Theories at a Lifshitz point: Chen & Huang PLB(10)-a0904 [UV behavior];
Iengo et al JHEP(09)-a0906 [one-loop renormalization].
> Gravity-related
theories: see covariant quantum gravity;
gravitational constant [running];
quantum-gravity renormalization.
> Other types of theories:
see gauge theories; quantum field
theory in curved spacetime; stress-energy tensor;
Thirring Model.
> Related topics:
see boundaries; Coarse-Graining;
Coarse Structures in Geometry;
path integrals; quantum field theory;
renormalization group; sigma model.
> Applications:
see brownian motion; chaos;
entanglement; phase transitions;
probability theory.
Scalar Field Theories
> s.a. inflationary models.
* Renormalizability types:
Covariant scalar field theory models are either super renormalizable, strictly
renormalizable, or nonrenormalizable, but mixed models can be constructed.
@ General references:
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-conf [in E3];
Casadio IJMPA(12)-a0806 [gravitational renormalization];
Mohammedi a1306 [field redefinition and renormalizability];
Litim & Trott PRD(18)-a1810 [asymptotic safety];
Balakumar & Winstanley a1910 [Hadamard renormalization].
@ φ^4 theory:
Pinter AdP(01) [Epstein-Glaser approach];
de Albuquerque ht/05 [with Robin boundary conditions];
de Aragão & Carneiro PLA(06) [by scaling];
Suslov ANM-a0911-conf
[beta function, strong-coupling asymptotics];
Adzhemyan & Kompaniets JPCS(14)-a1309 [numerical evaluation of critical exponents];
Jack & Poole PRD(18)-a1806 [4D, renormalisation scheme invariants];
Delcamp & Tilloy a2003 [using tensor networks];
> s.a. non-renormalizable theories below.
@ Other theories: Zanusso et al PLB(10)-a0904 [Yukawa and quartic, gravitational corrections];
Klauder IJMPA(17)-a1605 [with mixed renormalizability properties];
Juárez et al a2104 [two interacting scalar fields].
@ In curved spacetime: Bonanno PRD(95)gq [Einstein universe];
Hollands & Wald CMP(03)gq/02 [Klein-Gordon theory];
Kopper & Müller CMP(07) [φ4 on Riemanian manifolds];
Matsueda a1106;
Markkanen & Tranberg JCAP(13)-a1303 [one-loop renormalization, simple method];
Shapiro et al a1503
[with non-minimal interaction, functional renormalization group].
Non-Renormalizable Theories, Asymptotic Safety
* Idea: Some
perturbatively non-renormalizable theories define interacting quantum
field theories valid to arbitrarily high momentum scales because of the
existence of a non-Gaussian fixed point (Weinberg's asymptotic safety);
Examples are the 2 < D < 4 Gross-Neveu model, the
non-linear σ-model, the sine-Gordon model and Einstein gravity.
@ General references:
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];
Kazakov & Vartanov JPA(06),
ht/06 [renormalizable expansions];
Klauder AP(07)ht/06 [new approach];
Klauder JPA(08)-a0805 [divergence-free],
JPA(09)-a0811,
a0904-in [approach];
Sonoda a0909 [continuum limit];
Dvali et al JHEP(11)-a1010 [UV completion by classicalization];
Pittau FdP(15)-a1305 [predictivity],
a1311-conf [FDR approach].
@ Asymptotic safety: Nagy AP(14)-a1211-ln [and the functional renormalization group method];
Rischke & Sannino PRD(15)-a1505 [thermodynamics];
Intriligator & Sannino JHEP(15)-a1508 [in supersymmetric theories];
Mann et al PRL(17)-a1707,
Pelaggi et al PRD(18)-a1708 [asymptotically safe extensions of the Standard Model];
Bond & Litim PRL(19)-a1801 [and non-abelian gauge interactions];
Barducci et al JHEP(18)-a1807
[UV completions of the Standard Model that don't work];
> s.a. renormalization of gauge theories [QED].
@ Gravity: Barvinsky et al PRD(93)gq [with a scalar field];
> s.a. asymptotic safety in quantum gravity.
@ Other types of theories: Klauder LMP(03)ht/02
[φ4n
theories, n ≥ 4],
JSP(04)ht/03
[φp3,
p = 8, 10, 12, ...];
Anselmi JHEP(05)ht [class including all self-interacting scalars];
Braun et al PRD(11)-a1011 [Gross-Neveu model];
Cahill PRD(13)-a1303 [some are well-behaved];
Litim & Sannino JHEP(14)-a1407
[cooperation between non-abelian gauge fields, fermions and scalars];
Polyakov et al TMP(19)-a1811 [quasi-renormalizable field theories].
Other Theories > s.a. Disorder.
@ Non-commutative theories:
Gayral et al PLB(05)ht/04 [possible trouble];
Rivasseau et al CMP(06)ht/05 [φ4];
Grosse & Steinacker NPB(06)ht/05 [φ3],
ATMP(08)ht/06 [6D φ3];
Grosse & Wohlgenannt JPCS(07)ht/06;
Vignes-Tourneret PhD(06)mp;
Rivasseau & Vignes-Tourneret ht/07-conf;
Rivasseau in(07)-a0705 [rev];
Gurău & Tanasă AHP(08)-a0706 [and dimensional regularization];
Tanasă & Vignes-Tourneret JNCG(08)-a0707 [Hopf algebra structure];
Gurău a0711-en
[φ4*4];
Gurău PhD(07)-a0802;
Sfondrini & Koslowski IJMPA(11)-a1006 [scalar, functional renormalization];
PRD(13)-a1207
[φ4 scalar field on the Groenewold-Moyal plane];
Blaschke FdP(14)-a1402-conf [renormalizable theories];
> s.a. renormalization of gauge theories.
@ Hamiltonian field theories:
Maslov & Shvedov ht/98-conf;
Lieneger & Thiemann a2003 [free vector bosons].
@ Group field theories:
Carrozza PhD(13)-a1310,
Sigma(16)-a1603;
> s.a. renormalization of quantum gravity.
@ Other types:
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];
Tu & Sanz PRB(10)-a1005 [quantum spin chains];
Corichi & Vukašinac PRD(12)-a1202 [constrained theories, polymer approach];
Cenatiempo & Giuliani JSP(14)-a1404 [2D Bose gas, critical point];
Khavkine & Moretti CMP(16)-a1411
[locally covariant theories, continuity and analyticity hypotheses are unnecessary];
Green & Moffat a2012 [finite quantum field theory].
@ Modified theories:
Bezerra et al PRD(04) [deformed];
Anselmi & Halat PRD(07) [Lorentz-violating];
López & Mazzitelli PLB(09)-a0810,
Mazzitelli IJMPD(11) [with modified dispersion relations];
Sathiapalan IJMPA(13)-a1306 [closed string theory].
> Online resources:
see PI talks
on Renormalization in Background Independent Theories.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
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