Unified Theories

In General
* 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].

Unification of Interactions > s.a. interactions.
* 1800's: Unification in the modern sense started with Maxwell's unification of electricity and magnetism.
* 1900's: 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 1970's; 1970's, 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, consensus seems to be that it won't work.
* 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.
@ History: 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].
@ Related topics: Weinberg SA(99)dec [future]; Myrvold PhSc(03) [advantages, Bayesian view].

Gravitation and Electromagnetism > s.a. kaluza-klein; teleparallel theories; tests of general relativity.
* Idea: Either (i) Give up the geometrical description of gravity, or (ii) Describe the other forces geometrically, as in the Kaluza-Klein idea.
* Weyl's theory: Unifies gravity and electromagnetism in terms of a conformal geometry and a connection, with conformal changes in the metric being "gauge," the conformal degree of freedom being related to electromagnetism; It implied that clock rates depend on clock world-lines, which is incompatible with observation; In Dirac's reformulation, the action is much simpler than Weyl's, but it requires a scalar field function to describe the gravitational field, in addition to the metric, and the theory becomes a scalar-tensor one; > s.a. conformal invariance.
@ Weyl's theory: Weyl SPAW(18), AdP(19), Nat(21)feb; in Weyl 52; in Adler, Bazin & Schiffer 75; Elizondo & Yepes ApJ(94)ap/93 [and cosmology]; Boulanger & Henneaux AdP(01)ht-in [uniqueness]; Israelit FP(05)-a0710 [measurement standards].
@ Weyl-Dirac theory: Dirac PRS(73); Israelit 99; Mirabotalebi & Jalalzadeh gq/05 [as dark matter alternative].
@ Weyl's theory, variations: Pullin & Bressan GRG(87) [modified]; Puetzfeld & Tresguerres CQG(01)gq [Weyl-Cartan, cosmology]; Flanagan PRD(06)ap [fourth-order]; Barabash & Pyatkovska a0709 [Mannheim's proposal, weak-field limit phenomenology].
@ Einstein's unified theory: Einstein SPAW(25), SPAW(28), MA(30) [translation Unzicker & Case phy/05]; Tonnelat 55; Voros AusJP(95)gq [non-symmetric g]; Antoci AFLB(96)gq/98 [geometry and fields]; Sauer HM(06)phy/04 [Einstein's Fernparallelismus]; Antoci et al GRG(05)gq/04 [electrostatics]; von Borzeszkowski & Treder FP(04) [and alternative geometries]; Chamseddine ht/06-in [generalization to complex hermitian spacetime]; Antoci et al gq/07-in [and sources]; Antoci & Liebscher a0706 [Treder and confinement]; > s.a. modified electrodynamics.
@ Other proposals: Misner & Wheeler AP(57) [geometrical]; Lanczos JMP(67); Mikhail & Wanas PRS(77), IJTP(81), Wanas ASS(89) [tetrad-based]; Ferraris & Kijowski GRG(82) [based on linear connection]; Beil IJTP(87) [5th timelike dimension, velocity-dependent metric]; Miron & Radivoiovici-Tatoiu RPMP(89) [Finsler-based]; Searight GRG(03)ht/04 [based on degenerate metrics]; Wanas & Ammar gq/05 [based on parametrized absolute parallelism]; Chernitskii G&C(06)ht [4-vector field]; Vignolo & Massa CQG(06) [5D, vielbein formulation]; Poplawski gq/06, a0705, a0801 [affine theory], a0803 [Eisenhart's metric-affine theory]; Hehl FP(08)phy/07, & Obukhov FP(08)phy/07 [re Evans' theory].

Other Unified Theories > s.a. gravity theories; GUTs; particle physics; string theory.
@ 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-in [geometrical, Kaluza-Klein]; Glinka & Pervushin a0705; Nesti & Percacci a0706 [graviweak]; Alexander a0706 [isogravity].
@ Gravity + standard model: Pawlowski hp/96; Lisi gq/05 [Clifford bundle formulation], a0711 + pw(08)jul [E8 connection formulation]; Nesti a0706 [using spinors].
@ Gravity + other theories: Bergmann in(81); Dell & Smolin in(86) [metric-connection]; Peldán NPB(93)gq/92 [+ Yang-Mills]; Ackermann & Tolksdorf ht/95 [+ Yang-Mills-Higgs]; Gogoladze et al PRL(03) [all gauge theories, higher-dimensional]; Patwardhan ht/04 [gauge theory of all interactions]; Smolin a0712 [+ Yang-Mills, extended Plebanski action].
@ Related topics: Chrusciel AIHP(85); Özer gq/99, gq/00 [and equivalence principle, cosmological constant]; Aldaya et al JPA(02)ht/01 [group cohomology].

Main page – Abbreviations – Journals – Comments – Other sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified 20 jul 2008