Unified Theories

In General > s.a. paradigms in physics; physical theories [ToEs, Theories of Everything]; quantum gravity and approaches [gravity and quantum theory].
* Idea: Unification may refer to the merging of conceptual and technical frameworks from different theories, a tradition that can be traced back to the celestial/earthly world unification of the 1500s and 1600s, or to the unification of two interactions that results when they are included in a larger theory.
* Examples: Keplerian orbits + Galilean physics → Newtonian mechanics; Maxwell theory + Galilean relativity → special relativity; Special relativity + non-relativistic quantum mechanics → antiparticles; Special relativity + Newtonian gravity → general relativity; Quantum theory + general relativity → ???
@ References: Rueger BJPS(05) [and scientific realism]; Schellekens RPP(08)-a0807 [rev]; Hawking & Mlodinow SA(10)oct [ToE]; news nat(11)mar [status]; Emam 11; Kim a1301-conf [historical approach]; Wilczek PTRS(16)-a1512-talk [Maxwell and the unity of field and substance]; Langacker 17.

Unification of Fundamental Interactions > s.a. GUTs; interactions; Relativity Principle; symmetries in physics.
* 1800s: Unification in the modern sense started with Maxwell's unification of electricity and magnetism.
* 1900s: Kaluza, Klein, and Einstein worked on unifying electromagnetism with gravitation when those were the only two known forces; Because of the lack of a clear success (despite interesting ideas) and the interest in nuclear interactions, after 1955 not many people worked on unification until the 1970s; 1970s, Salam-Weinberg electroweak theory, and higher-dimensional supersymmetry and supergravity; 1984, Strings replace d = 11 supergravity as favorite TOE; 1996, M-theory replaces the 5 consistent string theories; 1999, Randall-Sundrum and other models introduce the brane-world idea.
* 2008: Garrett Lisi proposed a theory based on an E8 connection; After a few months, the consensus seems to be that it won't work.
* 2018: The geometric unification of gravity with the other interactions is not currently the most popular approach; It is generally believed that if a unified theory is possible it will emerge in the process of quantizing gravity (string theory) or it will be constructed once a quantum theory of gravity is available (lqg).
* Scales: Electroweak unification at about 10³ GeV, GUT unification at perhaps 10¹⁶ GeV, with gravity at possibly 10¹⁹ GeV, the Planck energy; The disparity between these energy scales gives rise to the hierarchy problem.
* Rem: In the most common unified scenarios, interactions are unified at very high energies when the various coupling constants approach the same value and the theory has a symmetry group that includes the ones of the individual interactions; But this picture may lose its motivation if the continuum disappears at high energies.
@ General references: Weinberg SA(99)dec [future]; Myrvold PhSc(03)apr [advantages, Bayesian view]; Ha a1007-conf [status, issues]; Krasnov & Percacci CQG(18) and CQG+(18) [rev, and arguments for unifying before quantizing]; Delphenich a1811-proc [premature unification, unification vs concatenation vs formal analogy].
@ History: Gell-Mann et al in(79)-a1307 [several possibilities]; Goenner LRR(04); Verbin & Nielsen GRG(05)phy/04 [Kaluza's idea]; Ducheyne SHPSA(05) [and Newton]; Battimelli EJP(05) [and pre-Einstein electromagnetism]; Ellis pw(05)jan [Einstein]; Regge JPA(07) [thoughts on future]; Collins SA(08)apr [Lisi's proposal]; van Dongen 10 [Einstein's attempts, r Isis(11)#4 Schweber]; Goenner LRR(14) [part II, 1930-1965]; Nath 16; Nanni ASTP(19)-a1803 [Fermi theory of beta decay]; in Halpern PT(19)apr [Einstein's attempts]; > s.a. GUTs; history of physics.
@ Geometrical aspects: Cirilo-Lombardo IJTP-a1411 [possible fermionic representations, algebraic and geometrical viewpoints]; Roldan & Barros a1603.
@ Related topics: Wilczek PT(01) [coupling constant unification]; Shaposhnikov & Wetterich PLB(10) [Higgs self-coupling flows to zero near the Planck scale]; Ferreira et al PLB(13) [using the radio source PKS1413+135]; 't Hooft FP(14) [and the ontological interpretation of quantum mechanics]; Finster & Kleiner JPCS(15)-a1502, Finster a1505 [causal fermion systems].

Specific Unified Theories > s.a. gravity + electromagnetism; gravity theories; particle physics; string theory.
* Gravity + standard model: One common approach is to treat gravity as a gauge theory with tetrads and spin-connections as variables.
@ Gravity + electroweak: Verwimp JMP(90); Gitner & Dehnen NCB(00)gq/97 [parity violation]; Batakis PLB(97)ht/96; Cianfrani & Montani IJTP(07)gq/06, gq/06-MGXI [geometrical, Kaluza-Klein approach]; Glinka & Pervushin ONCP(08)-a0705; Nesti & Percacci JPA(08)-a0706 [graviweak]; Alexander a0706 [isogravity]; Pandres GRG(09)-a1006 [replacing diffeomorphisms with larger group]; Scholz AdP(11)-a1102 [extended Weyl theory]; Hsu MPLA(11)-a1106; Onofrio MPLA(14)-a1412 [gravitoweak unification].
@ Gravity + standard model: Pawłowski hp/96; Gillan ht/01 [with 3 timelike dimensions]; Patwardhan ht/04 [gauge theory of all interactions]; Lisi gq/05 [Clifford-bundle formulation], a0711 + pw(08)jul [E8 connection formulation]; Nesti a0706 [using spinors]; Jones SHPMP(09) [evidence for one does not disconfirm the other]; Distler & Garibaldi CMP(10)-a0905 [E8 is not enough]; Lisi et al JPA(10)-a1004; Lisi a1006-proc [embedding in E8]; Lisi & Weatherall SA(10)dec; Andrianov et al PRL(13)-a1302 [Universal Landau Pole]; Hsu ChJP-a1309 [based on gauge theory of the translation group]; Delbourgo IJMPA(13) [with fermionic Lorentz scalar variables]; Finster a1409 [from continuum limit of system with massive Dirac particles and neutrinos]; Stack & Delbourgo IJMPA(15)-a1511 [gravity + chromodynamics with 3 anticommuting color coordinates]; Delbourgo in(16)-a1602 [bosonic spacetime plus fermionic property space]; Mannheim IJMPD(16)-a1603-GRF [geometrization of all interactions, using conformal gravity]; Chkareuli PRD(17)-a1703 [Poincaré gauge gravity]; Radenković & Vojinović a2103 [higher gauge theory framework]; > s.a. spin-foam models.
@ Gravity + Yang-Mills theory: Peldán NPB(93)gq/92; Ackermann & Tolksdorf ht/95 [+ Higgs field]; Gogoladze et al PRL(03) [higher-dimensional]; Smolin PRD(09)-a0712 [extended Plebański action]; Torres-Gomez & Krasnov PRD(10)-a0911 [+ Higgs field]; Elyasi & Boroojerdian a1109 [Lie-algebroid structures]; Alexander et al PLB(12)-a1105 [SU(2) and 3D general relativity, spin-foam approach]; Gerhardt ATMP(14)-a1207, a1301 [and spinor fields]; Stack & Delbourgo IJMPA(15)-a1411 [with anticommuting coordinates in the spacetime metric]; Chamseddine & Mukhanov JHEP(16)-a1602 [higher-dimensional Lorentz group as the symmetry of the tangent space]; Singh a2009 [trace dynamics and division algebras, in 8D octonionic space].
@ Gravity + other theories: Bergmann in(81); Dell & Smolin in(86) [metric-connection]; Alexandre et al NJP(10)-a0906 [N = 8, D = 4 supergravity as ToE]; Pavšič JPCS(10)-a0912; Krasnov & Percacci CQG(18)-a1712 [classical, rev]; > s.a. spin-foam models.
@ Related topics: Chruściel AIHP(85); Samokhvalov & Vanyashin CQG(91)-a1802 [deformed spacetime diffeomorphisms]; Özer gq/99, gq/00 [and the equivalence principle, cosmological constant]; Aldaya et al JPA(02)ht/01 [group cohomology]; Aranda & Wudka PRD(10)-a1008 [gauge-Higgs]; Vieira et al PRD(12)-a1206 [solar-type main-sequence stars as probes]; Ootsuka a1206 [in terms of Kawaguchi areal geometry]; Furey PRD(12) [unified theory of ideals]; Cirilo-Lombardo et al IJTP-a1404 [based on affine geometry]; Reig et al PLB(17)-a1706 [comprehensive unification using fermions].
> Related topics: see electroweak theory; GUTs [electroweak and strong interactions]; non-commutative gravity and gauge theories.

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