Fine-Structure Constant  

In General > s.a. variation of constants; bounds on fine-structure constant variation.
* History and value: The constant, introduced by Sommerfeld in 1916 in his study of the hydrogen atom, αQED:= e2/\(\hbar\)c = 7.297 352 568(24) × 10−3 = 1/137.03599976... ≈ 1/137; 2006 experimental value α−1 = 137.035 999 710 (96); 2008 experimental value 137.035 999 084 (51).
* Running, renormalization: At about 100 GeV (LEP energies), the value is 1/128.9; It should keep growing at higher energies, and diverge at a very high but finite energy (> Landau-Pole Problem; renormalization).
@ General articles: Lubkin PT(71)aug, letter PT(71)nov, Adawi et al PT(90)dec; Gross PT(89)dec; Nasseri PLB(05), PLB(06)ht/05 [corrections from gup]; Seidel NCB(06) [statistical approach]; Davies IJTP(08)-a0708 [and gravitational thermodynamics]; Gogberashvili & Kanatchikov a1009 [in a Machian universe]; Mainland & Mulligan a1705 [theoretical calculation].
@ Measurement: Gabrielse et al PRL(06), news pn(06)jun and pw(06)aug [best]; Hanneke et al PRL(08) [best]; Maciejko et al PRL(10) [using a topological insulator]; Bouchendira et al AdP(13)-a1309 [state of the art].
@ Running, renormalization: Levine et al PRL(97) [evidence]; Tobar Met-hp/03 [and flux quanta]; Toms PRL(08)-a0809 [quantum gravity corrections]; Eichhorn et al PLB(18)-a1711 [quantum-gravity predictions, asymptotic safety].
@ Anthropic arguments: Eaves PhyA(16)-a1412 [anthropic fine-tuning]; Sandora JCAP(16)-a1604 [anthropic requirements for habitable planets].
@ Related topics: Jentschura PRA(14)-a1404 [gravitational fine-structure constant αG = Gm1m2/\(\hbar\)c].
@ Variation, reviews: Fiorentini & Ricci ESO(03)ap/02; Murphy et al eConf-ap/02; Martins ap/04-proc; Scóccola PhD(09)-a0906 [and electron mass].

Variation, Theory > s.a. cosmological constant / cosmology in modified gravity; dark matter; FLRW models; higher-order gravity.
* History: Dirac (1937) and Landau (1955) proposed that α could vary in time.
* Idea: Variations can be driven by changes in the relationship between electric and magnetic field energies.
@ General references: Bekenstein PRD(82) [framework]; Karshenboim GRG(06) [search methods]; Barrow AdP(10)-a0912-proc [rev].
@ And quintessence: Huey et al PRD(02)ap/01 [and cmb]; Anchordoqui & Goldberg PRD(03)hp; Lee et al IJMPD(05)ap/03 [bound]; Bento et al PRD(04)ap [2-field]; Marra & Rosati JCAP(05)ap; Avelino et al JCAP(06); Lee MPLA(07)ap [and mp/me]; Bento & González PLB(09).
@ And dark matter: Olive & Pospelov PRD(02)hp/01 [+ Λ]; Barnett et al MNRAS(04)ap [dark matter oscillations]; Stadnik & Flambaum PRL(15)-a1503.
@ And spectroscopy: Dzuba & al PRL(99)phy/98, PRA(99)phy/98; Bekenstein ap/03.
@ And the cosmological constant: Kühne MPLA(99) [α-dot implies Λ]; Fujii ASS(03)gq/02-conf.
@ Other: Barrow & Magueijo PLB(98)ap; Bergström et al PRD(99)ap [nucleosynthesis]; Banks et al PRL(02) [and quantum field theory]; Damour ASS(03)gq/02-conf, Gregori hp/02 [string theory]; Barrow & Mota CQG(03)gq/02 [perturbations]; Rañada EPL(03)ap/02 [as quantum field theory vacuum effect]; Bekenstein PRD(02)gq [and equivalence principle]; Rafelski hp/02 [non-universal gravity]; Tobar Met-hp/03 [electromagnetic constants]; Steinhardt PRD(05)hp/03 [constraints]; Belinchón gq/04; Kimberly & Magueijo PLB(04)hp/03 [and the standard model]; Kozlov et al PRA(04)ap [and variation of isotope abundances]; Campanelli et al MPLA(07)ap/05 [and domain walls]; Fujii PLB(08)-a0709 [scalar-tensor theory, and acceleration]; Anchordoqui et al PLB(08) [phase transition at z = 0.5]; Bekenstein & Schiffer PRD(09)-a0906 [and black holes]; MacGibbon a1003-MG12 [and generalized second law]; Barrow & Lip PRD(12)-a1110 [generalized theory]; Sloan CQG(14)-a1307 [in lqc].
@ Spatial variation: Barrow et al PRD(02)ap; Mota & Barrow MNRAS(04)ap/03; Parkinson et al PLB(04)ap/03 [mapping the dark energy]; Sigurdson et al PRD(03)ap [and cmb]; Mota PhD(03)ap/04 [BSDM theory]; Olive et al PRD(11)-a1011 [and domain walls]; Barrow & Magueijo MPLA(15)-a1412.
@ And variation of c: Barrow & Magueijo ApJL(00)ap/99; Davies et al Nat(02)aug, refuted by Duff ht/02 (refuted by Moffat ht/02), Flambaum ap/02, Carlip & Vaidya Nat(03)ht/02; Magueijo et al PLB(02)ap; Peres IJMPD(03)qp/02, gq/02 [theory]; Alfonso-Faus gq/02/EJP [no].
@ No variation, alternative interpretations: Sumner ap/05 [and no cosmological constant!]; Bandiera & Corbelli A&A(05)ap [mimicked by correlations?]; Chang et al EPJC(12)-a1106 [spacetime anisotropy].
> Related topics: see black-hole thermodynamics; inflationary phenomenology; modified electrodynamics [non-linear]; particles [electron mass].

Variation, Consequences > s.a. modified lorentz symmetry.
* Idea: It would imply a non-expansion contribution to redshift, the splitting between atomic energy levels in quasar spectra, and the existence of an ultralight scalar particle; But probably not to a violation of the weak equivalence principle; It would affect stellar nucleosynthesis, a 4% increase in α would effectively shut down C production in stars.
@ General references: Berman & Trevisan gq/02; Dvali & Zaldarriaga PRL(02) [5th force and 5essence]; Langacker et al PLB(02) [variations in ΛQCD]; Carlip PRD(03)gq/02 [black holes and quantum gravity]; Tobar & Hartnett PRD(03)gq [proposed experiment]; Bertolami & Monteiro PRD(05) [and primordial B fields]; Flambaum PRA(06), Flambaum & Kozlov PRL(07), Beloy et al PRA(10) [diatomic molecules].
@ And black-hole thermodynamics: Das & Kunstatter CQG(03)ht/02; Fairbairn & Tytgat JHEP(03)ht/02 [Reissner-Nordström black-hole entropy].

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