Applied Mathematics & Optimization

, Volume 69, Issue 3, pp 359–392 | Cite as

Unified Field Theory and Principle of Representation Invariance

Article

Abstract

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 energy-momentum 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,Wa,Sk), 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).

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 

References

  1. 1.
    Englert, F., Brout, R.: Broken symmetry and the mass of gauge vector mesons. Phys. Rev. Lett. 13(9), 321–323 (1964) CrossRefMathSciNetGoogle Scholar
  2. 2.
    Glashow, S.: Gauge theories of vector particles. DOE technical report (1961) Google Scholar
  3. 3.
    Griffiths, D.: Introduction to Elementary Particles. Wiley-VCH, New York (2008) Google Scholar
  4. 4.
    Guralnik, G., Hagen, C.R., Kibble, T.W.B.: Global conservation laws and massless particles. Phys. Rev. Lett. 13(20), 585–587 (1964) CrossRefGoogle Scholar
  5. 5.
    Halzen, F., Martin, A.D.: Quarks and Leptons: an Introductory Course in Modern Particle Physics. Wiley, New York (1984) Google Scholar
  6. 6.
    Higgs, P.W.: Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett. 13, 508–509 (1964) CrossRefMathSciNetGoogle Scholar
  7. 7.
    Kaku, M.: Quantum Field Theory, a Modern Introduction. Oxford University Press, London (1993) Google Scholar
  8. 8.
    Kane, G.: Modern Elementary Particle Physics vol. 2. Addison-Wesley, Reading (1987) Google Scholar
  9. 9.
    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
  10. 10.
    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
  11. 11.
    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 CrossRefMATHGoogle Scholar
  12. 12.
    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
  13. 13.
    Ma, T., Wang, S.: Unified field equations coupling four forces and principle of interaction dynamics. arXiv:1210.0448 (2012)
  14. 14.
    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
  15. 15.
    Nambu, Y.: Spontaneous symmetry breaking in particle physics: a case of cross fertilization (2008). http://www.nobelprize.org/nobel_prizes/physics/laureates/2008/nambu-slides.pdf
  16. 16.
    Quigg, C.: Gauge Theories of the Strong, Weak, and Electromagnetic Interactions. Benjamin/Cummings, Reading (1983) Google Scholar
  17. 17.
    Salam, A.: Elementary Particle Theory. Svaratholm, Stockholm (1968) Google Scholar
  18. 18.
    Weinberg, S.: A model of leptons. Phys. Rev. Lett. 19, 1264–1266 (1967) CrossRefGoogle Scholar
  19. 19.
    Zhang, N.-S.: Particle Physics, vol. I & II. Chinese Academic Press, Beijing (1994). In Chinese Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduP.R. China
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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