Unified Theories of Gravity and Electromagnetism  

In General > s.a. other unified theories.
* Idea: These are proposals for unifying gravity and electromagnetism before quantizing the theories.
* Options: Either (i) Give up the geometrical description of gravity, or (ii) Describe the other forces geometrically, as in the Kaluza-Klein idea.
@ General references: Bertolami a1005-conf [historical]; Vaugon et al a1010 [higher-dimensional, a mathematicians' view].
> Related topics: see kaluza-klein theory; post-newtonian gravity; teleparallel theories; tests of general relativity.

Weyl's Theory > s.a. modified theories of quantum gravity; Weyl Geometry.
* Idea: It 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.
@ General references: Weyl SPAW(18), AdP(19), Nat(21)feb; in Weyl 52; in Adler, Bazin & Schiffer 75; Boulanger & Henneaux AdP(01)ht-conf [uniqueness]; Israelit FP(05)-a0710 [measurement standards]; Afriat SHPMP(09) [history]; Wheeler PRD(14) [as general relativity]; Romero a1508-conf [revisiting Einstein's criticism]; Chen & Ma PRD(18)-a1803 [Hamiltonian structure and connection dynamics].
@ And general relativity: Romero et al CQG(12)-a1201; Ghilencea JHEP(19)-a1812 [symmetry breaking to Einstein theory]; Oda a2003 [quantum mechanical equivalence to Einstein's general relativity plus a massive Weyl gauge field].
@ Weyl-Dirac theory: Dirac PRS(73); Israelit 99; Mirabotalebi et al MNRAS(08)-gq/05 [as dark matter alternative].
@ Other variations: Pullin & Bressan GRG(87) [modified]; Flanagan PRD(06)ap [fourth-order]; Barabash & Pyatkovska UJP-a0709 [Mannheim's proposal, weak-field limit phenomenology]; Barceló et al JCAP(17)-a1703 [improved theory]; > s.a. teleparallel gravity.
@ Cosmology: Elizondo & Yepes ApJ(94)ap/93; Puetzfeld & Tresguerres CQG(01)gq [Weyl-Cartan theory]; Maki et al APPB(10)-a1204; Jiménez & Koivisto PLB(16)-a1509 [inflation]; Deliduman et al a1511 [galaxy rotation curves].
@ Other phenomenology: Islam MNRAS(19)-a1811 [velocity dispersion profiles of galactic globular clusters].

Einstein's Unified Theory
@ General references: Einstein SPAW(25), SPAW(28), MA(30) [translation Unzicker & Case phy/05]; Tonnelat 55; 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]; Antoci et al AFLB(08)gq/06 [confinement], in(08)gq/07 [and sources]; Antoci & Liebscher a0706 [Treder and confinement]; Sauer & Schütz a2008; > s.a. modified electrodynamics.
@ Non-symmetric g: Voros AusJP(95)gq; Hammond a1901 [and torsion].
@ Variations: Chamseddine in(06)ht [generalization to complex hermitian spacetime].

Other Proposals > s.a. quaternions; torsion in physics.
@ Geometrical: Misner & Wheeler AP(57); Ferraris & Kijowski GRG(82) [based on linear connection]; Belabbas PhD(11)-a1401.
@ General references: Lanczos JMP(67); Mikhail & Wanas PRS(77), IJTP(81), Wanas ASS(89) [tetrad-based]; Miron & Radivoiovici-Tatoiu RPMP(89) [Finsler-based]; Samokhvalov PNPCR(91)-a1802 [group theory approach]; Özer gq/99 [and equivalence principle for the electromagnetic field]; Searight GRG(03)ht/04 [based on degenerate metrics]; Wanas & Ammar MPLA(10)gq/05 [based on parametrized absolute parallelism]; Chernitskii G&C(06)ht [4-vector field]; Hehl FP(08)phy/07, & Obukhov FP(08)phy/07 [re Evans' theory]; Borzou & Sepangi a0902; Giglio & Rodrigues AACA-a1109 [Riemann-Cartan structure]; Voicu a1111 [tidal tensors and connections on the tangent bundle]; Chew a1209.
@ With a 5th dimension: Beil IJTP(87) [5th timelike dimension, velocity-dependent metric]; Vignolo & Massa CQG(06) [5D, vielbein formulation]; Li FrPh(16)-a1511 [4D spacetime as a hypersurface]; > s.a. kaluza-klein theory.
@ With non-linear electrodynamics: Chernitskii in(08)-a1006, G&C(09)-a0907-in [and effective metric], G&C(11)-a1106 [and gravitational field screening]; Torres-Gómez et al PRD(11)-a1011 [BF-type theory].
@ From affine geometries: Popławski IJMPD(09)gq/06, a0705, MPLA(09)-a0801; Popławski IJMPA(09)-a0803 [Eisenhart's metric-affine theory]; Elyasi & Boroojerdian IJTP(11); Cirilo-Lombardo IJTP(11).
@ Non-symmetric affine connections: Ghose a1302-wd [Bose's theory]; Alhamzawi & Alhamzawi a1405; Ghose a1408; Kharuk et al G&C(18)-a1709; Kharuk et al EPJwc(17)-a1803.
@ Phenomenology: Ghose a1408 [Mach's principle and cosmology].

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