Unified Field Theory and Principle of Representation Invariance
 Tian Ma,
 Shouhong Wang
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The main objectives of this article are to postulate a new principle of representation invariance (PRI), and to refine the unified field model of four interactions, derived using the principle of interaction dynamics (PID). Intuitively, PID takes the variation of the action functional under energymomentum conservation constraint, and PRI requires that physical laws be independent of representations of the gauge groups. One important outcome of this unified field model is a natural duality between the interacting fields (g,A,W ^{ a },S ^{ k }), corresponding to graviton, photon, intermediate vector bosons W ^{±} and Z and gluons, and the adjoint bosonic fields \((\varPhi_{\mu}, \phi^{0}, \phi^{a}_{w}, \phi^{k}_{s})\) . This duality predicts two Higgs particles of similar mass with one due to weak interaction and the other due to strong interaction. The unified field model can be naturally decoupled to study individual interactions, leading to (1) modified Einstein equations, giving rise to a unified theory for dark matter and dark energy (Ma and Wang in Discrete Contin. Dyn. Syst., Ser A. 34(2):335–366, 2014), (2) three levels of strong interaction potentials for quark, nucleon/hadron, and atom respectively (Ma and Wang in Duality theory of strong interaction, 2012), and (3) two weak interaction potentials (Ma and Wang in Duality theory of weak interaction, 2012). These potential/force formulas offer a clear mechanism for both quark confinement and asymptotic freedom—a longstanding problem in particle physics (Ma and Wang in Duality theory of strong interaction, 2012).
 Englert, F., Brout, R.: Broken symmetry and the mass of gauge vector mesons. Phys. Rev. Lett. 13(9), 321–323 (1964) CrossRef
 Glashow, S.: Gauge theories of vector particles. DOE technical report (1961)
 Griffiths, D.: Introduction to Elementary Particles. WileyVCH, New York (2008)
 Guralnik, G., Hagen, C.R., Kibble, T.W.B.: Global conservation laws and massless particles. Phys. Rev. Lett. 13(20), 585–587 (1964) CrossRef
 Halzen, F., Martin, A.D.: Quarks and Leptons: an Introductory Course in Modern Particle Physics. Wiley, New York (1984)
 Higgs, P.W.: Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett. 13, 508–509 (1964) CrossRef
 Kaku, M.: Quantum Field Theory, a Modern Introduction. Oxford University Press, London (1993)
 Kane, G.: Modern Elementary Particle Physics vol. 2. AddisonWesley, Reading (1987)
 Ma, T., Wang, S.: Duality theory of strong interaction. Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series #1301 (2012). http://www.indiana.edu/~iscam/preprint/1301.pdf. See also: arXiv:1212.4893
 Ma, T., Wang, S.: Duality theory of weak interaction. Indiana University Institute for Scientific Computing. and Applied Mathematics Preprint Series. #1302 (2012). http://www.indiana.edu/~iscam/preprint/1302.pdf. See also: arXiv:1212.4893
 Ma, T., Wang, S.: Gravitational field equations and theory of dark matter and dark energy. Discrete Contin. Dyn. Syst., Ser. A 34(2), 335–366 (2014). See also arXiv:1206.5078 CrossRef
 Ma, T., Wang, S.: Structure and stability of matter. Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series #1303 (2012). http://www.indiana.edu/~iscam/preprint/1303.pdf. See also: arXiv:1212.4893
 Ma, T., Wang, S.: Unified field equations coupling four forces and principle of interaction dynamics. arXiv:1210.0448 (2012)
 Ma, T., Wang, S.: Weakton model of elementary particles and decay mechanisms. Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series #1304 (May 30, 2013). http://www.indiana.edu/~iscam/preprint/1304.pdf. See also: arXiv:1212.4893
 Nambu, Y.: Spontaneous symmetry breaking in particle physics: a case of cross fertilization (2008). http://www.nobelprize.org/nobel_prizes/physics/laureates/2008/nambuslides.pdf
 Quigg, C.: Gauge Theories of the Strong, Weak, and Electromagnetic Interactions. Benjamin/Cummings, Reading (1983)
 Salam, A.: Elementary Particle Theory. Svaratholm, Stockholm (1968)
 Weinberg, S.: A model of leptons. Phys. Rev. Lett. 19, 1264–1266 (1967) CrossRef
 Zhang, N.S.: Particle Physics, vol. I & II. Chinese Academic Press, Beijing (1994). In Chinese
 Title
 Unified Field Theory and Principle of Representation Invariance
 Journal

Applied Mathematics & Optimization
Volume 69, Issue 3 , pp 359392
 Cover Date
 20140601
 DOI
 10.1007/s0024501392260
 Print ISSN
 00954616
 Online ISSN
 14320606
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Principle of Interaction Dynamics (PID)
 Principle of Representation Invariance (PRI)
 Unified field equations
 Duality theory of interactions
 Quark confinement
 Asymptotic freedom
 Higgs mechanism
 Higgs bosons
 Quark potential
 Nucleon potential
 Atom potential
 Weak interaction potential
 Strong interaction force formulas
 Weak interaction force formula
 Electroweak theory
 Authors

 Tian Ma ^{(1)}
 Shouhong Wang ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Sichuan University, Chengdu, P.R. China
 2. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA