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 [φ⁴_n theories, n ≥ 4], JSP(04)ht/03 [φ^p₃, 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.

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