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 10^{3} GeV, GUT unification
at perhaps 10^{16} GeV, with gravity at possibly
10^{19} 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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