### Unified Theories of Gravitational and Electromagnetic Fields in Riemannian Geometry and Higher Dimension

**DOI's assignment:**

*the author of the article can submit here a request for assignment of a DOI number to this resource!*

**Cost of the service: euros 10,00 (for a DOI)**

#### Abstract

Some unified theories on the gravitational and electromagnetic fields are researched. We investigate mainly two new geometric unified theories. A method is that the gravitational field and the source-free electromagnetic field can be unified by the equations Rklmi = κTklmi* in the Riemannian geometry, both are contractions of im and ik, respectively. If Rklmi = κTklmi* =constant, it will be equivalent to the Yang’s gravitational equations Rkm;l –Rkl;m = 0, which include Rlm= 0. From Rlm= 0 we can obtain the Lorentz equations of motion, the first system and second source-free system of Maxwell’s field equations. This unification can be included in the gauge theory, and the unified gauge group is SL(2,C) × U(1)=GL(2,C), which is just the same as the gauge group of the Riemannian manifold. Another unified method on the general nonsymmetric metric field with high-dimensional space-time and its matrix representations are analyzed mathematically. Further, the general unified theory of five-dimensional space-time combined quantum theory and four interactions is researched. Some possible unification ways on the gravitational and electromagnetic fields are discussed. The general matrix and various corresponding theories may decompose to a sum of symmetry and antisymmetry. Moreover, we proposed an imaginative representation on the ten dimensional space-time. *Copyright © 2014 Praise Worthy Prize - All rights reserved.*

#### Keywords

#### Full Text:

PDF#### References

O.Veblen and B.Hoffmann, Projective relativity. Phys.Rev. 36(1930), 810-822.

http://dx.doi.org/10.1103/physrev.36.810

A.Einstein, The Meaning of Relativity (Fifth edition). Princeton.1955.

http://dx.doi.org/10.1515/9781400851874

D.H.Boal and J.W.Moffat, Physical consequences of a solution of the nonsymmetric unified field theory. Phys.Rev. D11(1975),2026-2026.

http://dx.doi.org/10.1103/physrevd.11.2026

V.Hlavaty, Geometry of Einstain's Unified Field Theory. P.Noordhoff Ltd. 1957.

C.R.Johnson, Motion of Particles in Einstein's Relativistic Field Theory. Phys.Rev. D4(1971), 295-317; 318-339; 3555-3558; D5(1972), 282-284; 1916-1925; D7(1973), 2825-2837; 2838-2843; D8(1973), 1645-1651.

G.W.Gaffney, Electric and magnetic charge in Einstein's unified field theory. Phys.Rev. D10(1974),374-400.

http://dx.doi.org/10.1103/physrevd.10.374

J.W.Moffat and D.H.Boal, Solutions of the nonsymmetric unified field theory. Phys.Rev. D11(1975), 1375-1382.

http://dx.doi.org/10.1103/physrevd.11.1375

V.De Sabbata and E.Schmutzer, Unified Field Theories of More Than 4 Dimensions Including Exact Solutions: Proceedings. World Scientific. 1983.

J.Madore, Modification of Kaluza-Klein theory. Phys.Rev. D41(1990), 3709-3719.

http://dx.doi.org/10.1103/physrevd.41.3709

M.Chemtob, Systematics of string loop threshold corrections in orbifold models. Phys.Rev. D56(1997), 2323-2351.

http://dx.doi.org/10.1103/physrevd.56.2323

K.Dimopoulos, Primordial magnetic fields from superconducting cosmic strings. Phys.Rev. D57(1998),4629-4641.

http://dx.doi.org/10.1103/physrevd.57.4629

M.A.Luty, Weak scale supersymmetry without weak scale supergravity. Phys.Rev.Lett. 89(2002),141801. 1-4.

http://dx.doi.org/10.1103/physrevlett.89.141801

S.K.Solanki, O.Preuss, M.P.Haugan, et al. Solar constraints on new couplings between electromagnetism and gravity. Phys.Rev. D69(2004), 062001.1-11.

http://dx.doi.org/10.1103/physrevd.69.062001

X.Calmet, S.D.Hsu and D.Reeb, Grand unification and enhanced quantum gravitational effects. Phys.Rev.Lett. 101(2008),171802. 1-4.

http://dx.doi.org/10.1103/physrevlett.101.171802

Yi-Fang Chang, GRT extended for electromagnetic fields: equivalence principle and geometrization. Galilean Electrodynamics. 16(2005),91-96.

L.Landau and E.Lifshitz, The Classical Theory of Field. Cambridge, Mass. 1951.

http://dx.doi.org/10.1126/science.115.2990.425-a

P.G.Bergmann, Introduction to the Theory of Relativity. New York. 1947.

R.Utiyama, Invariant theoretical interpretation of interation. Phys.Rev. 101(1956), 1597-1607.

http://dx.doi.org/10.1103/physrev.101.1597

M.Carmili, Gauge fields and gravitational field equations. Nucl.Phys. B38(1972),621-627.

H.Yilmaz, New theory of gravitation. Phys.Rev.Lett. 27(1971), 1399-1402.

http://dx.doi.org/10.1103/physrevlett.27.1399

Yi-Fang Chang, New Research of Particle Physics and Relativity. Yunnan Science and Technology Press. 1989. p184-216. Phys.Abst. 93(1990), 1371.

Yi-Fang Chang, A unified scheme of four-interactions in particle physics and its Lagrangian. J.Xinyang Normal University. 17(2004), 1,30-34.

V.Fock, Theory of Space, Time and Gravitation. New York. 1959.

http://dx.doi.org/10.1126/science.133.3460.1248

C.Lanczos, Electricity and general relativity. Rev.Mod.Phys. 29(1957), 337-350.

http://dx.doi.org/10.1103/revmodphys.29.337

C.Lanczos, The splitting of the Riemann tensor. Rev.Mod.Phys. 34(1962),379-389.

http://dx.doi.org/10.1103/revmodphys.34.379

C.W.Kilmister and D.J.Newman, The use of algebraic structures in physics. Math.Proc.Cam.Phil.Soc. 57(1961),851-864.

http://dx.doi.org/10.1017/s0305004100036008

C.N.Yang, Integral formalism for gauge fields. Phys.Rev.Lett. 33(1974), 445-447.

http://dx.doi.org/10.1103/physrevlett.33.445

C.J.Isham, A.Salam and J.Strathdee, SL(6,C) gauge invariance of Einstein-like lagrangians. Nuovo Cimento. 5(1972),969-972.

http://dx.doi.org/10.1007/bf02798862

V.G.Kadyshevsky, R.M.Muradyan and A.N.Tavkhelidze, Relativistic generalization of SU (6)-symmetry. Phys.Lett. 15(1965),182-186.

http://dx.doi.org/10.1016/0031-9163(65)91332-6

C.Brans and R.H.Dicke, Mach's principle and a relativistic theory of gravitation. Phys.Rev. 124(1961),925-935.

http://dx.doi.org/10.1103/physrev.124.925

C.W.Misner, S.K.Thorne and J.A.Wheeler, Gravitation. W.H.Freeman and Company. 1973.

http://dx.doi.org/10.1002/asna.19752960110

G.Clement, A class of wormhole solutions to higher-dimensional general relativity. Gen.Rel.Grav. 16(1984),131-138.

http://dx.doi.org/10.1007/bf00762442

G.Clement, Axisymmetric regular multiwormhole solutions in five-dimensional general relativity. Gen.Rel.Grav. 16(1984),477-489.

http://dx.doi.org/10.1007/bf00762340

G.Clement, Massive from massless regular solutions in five-dimensional general relativity. Gen.Rel.Grav. 16(1984), 491-493.

http://dx.doi.org/10.1007/bf00762341

C.M.Misner, J.A.Wheeler, Classical physics as geometry. Ann.Phys. 2(1957),525-603.

http://dx.doi.org/10.1016/0003-4916(57)90049-0

J.A.Wheeler, On the nature of quantum geometrodynamics. Ann.Phys. 2(1957),604-614.

http://dx.doi.org/10.1016/0003-4916(57)90050-7

J.A.Wheeler, Geometrodynamics and the problem of motion. Rev.Mod.Phys. 33(1961),63 -78.

http://dx.doi.org/10.1103/revmodphys.33.63

Yi-Fang Chang, Geometric unifications of interactions, five-dimensional space-time and supersymmetry. J.Shangqiu Teachers College. 28(2012), 6,41-46.

Yi-Fang Chang, Velocity of light and relativity in very small space-time and some new equations of quantum mechanics. J.Yunnan University.33(2011),164-168.

Yi-Fang Chang, Extension and complete structure of the special relativity included superluminal and nutrino-photon with mass. Int.J.Mod.Theor.Phys. 2(2013),53-73.

T.Goldman, R.J.Hughes, M.M.Nieto, Experimental evidence for quantum gravity. Phys.Lett. B171(1986),217-222.

http://dx.doi.org/10.1016/0370-2693(86)91535-2

D.Garfinkle, General relativistic strings. Phys.Rev. D32(1985), 1323-1329.

http://dx.doi.org/10.1103/physrevd.32.1323

Yi-Fang Chang, Combination and incompatibility between quantum mechanics and relativity and their developments. J.Yunnan University. 30(2008),41-46.

Yi-Fang Chang, Relations between relativity and quantum Mechanics, and theoretical developments. J.Shangqiu Teachers College. 24(2008), 57-61.

Yi-Fang Chang, Negative matter, dark matter and theoretical test. Int.Rev.Phys. 5(2011),340-345.

Yi-Fang Chang, Basic laws on negative matter and its theoretical test as dark matter. J.Xinyang Normal University. 25(2012),3,299-304.

Yi-Fang Chang, Field equations of repulsive force between positive-negative matter, inflation cosmos and many worlds. Int.J.Mod.Theor.Phys. 2(2013),100-117.

Yi-Fang Chang, Development of Titius-Bode rule and cosmic quantum theory. Publ. Beijing Astron.Obs. 16(1990),16.

Yi-Fang Chang, Development of Titius-Bode law and the extensive quantum theory. Physics Essays. 15(2002),133-137.

http://dx.doi.org/10.4006/1.3025515

Yi-Fang Chang, Development of the extensive quantum theory and its applications in biology, chemistry and physics. J.Jishou Univ. 27(2006), 5, 34-38.

Yi-Fang Chang, Quantized phenomena in astronomy and astronomic quantum theory. Int.J.Sciences. 2(2013), 2,58-73.

Yi-Fang Chang, Nanophysics. macroscopic quantum phenomena and extensive quantum theory. Int.J.Nano and Material Sciences. 2(2013)1, 9-24.

### Refbacks

- There are currently no refbacks.

Please send any questions about this web site to info@praiseworthyprize.com**Copyright © 2005-2017 Praise Worthy Prize**