March  2015, 35(3): 1103-1138. doi: 10.3934/dcds.2015.35.1103

Unified field equations coupling four forces and principle of interaction dynamics

1. 

Department of Mathematics, Sichuan University, Chengdu

2. 

Department of Mathematics, Indiana University, Bloomington, IN 47405

Received  January 2013 Revised  July 2014 Published  October 2014

The main objective of this article is to postulate a principle of interaction dynamics (PID) and to derive field equations coupling the four fundamental interactions based on first principles. PID is a least action principle subject to div$_A$-free constraints for the variational element with $A$ being gauge potentials. The Lagrangian action is uniquely determined by 1) the principle of general relativity, 2) the $U(1)$, $SU(2)$ and $SU(3)$ gauge invariances, 3) the Lorentz invariance, and 4) the principle of representation invariance (PRI), introduced in [11]. The unified field equations are then derived using PID. The field model spontaneously breaks the gauge symmetries, and gives rise to a new mass generation mechanism. The unified field model introduces a natural duality between the mediators and their dual mediators, and can be easily decoupled to study each individual interaction when other interactions are negligible. The unified field model, together with PRI and PID applied to individual interactions, provides clear explanations and solutions to a number of outstanding challenges in physics and cosmology, including e.g. the dark energy and dark matter phenomena, the quark confinement, asymptotic freedom, short-range nature of both strong and weak interactions, decay mechanism of sub-atomic particles, baryon asymmetry, and the solar neutrino problem.
Citation: Tian Ma, Shouhong Wang. Unified field equations coupling four forces and principle of interaction dynamics. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 1103-1138. doi: 10.3934/dcds.2015.35.1103
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_______, Duality theory of strong interaction,, Electronic Journal of Theoretical Physics, (2014), 101. Google Scholar

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_______, Duality theory of weak interaction,, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, (2012). Google Scholar

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_______, Unified field theory and principle of representation invariance,, arXiv:1212.4893; version 1 appeared in Applied Mathematics and Optimization, 69 (2014), 359. doi: 10.1007/s00245-013-9226-0. Google Scholar

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_______, Gravitational field equations and theory of dark matter and dark energy,, Discrete and Continuous Dynamical Systems, 34 (2014), 335. Google Scholar

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_______, Weakton model of elementary particles and decay mechanisms,, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, (2013). Google Scholar

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Y. Nambu, Quasi-particles and gauge invariance in the theory of superconductivity,, Phys. Rev., 117 (1960), 648. doi: 10.1103/PhysRev.117.648. Google Scholar

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Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I,, Phys. Rev., 122 (1961), 345. doi: 10.1103/PhysRev.122.345. Google Scholar

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_______, Dynamical model of elementary particles based on an analogy with superconductivity. II,, Phys. Rev., 124 (1961), 246. Google Scholar

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C. Quigg, Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, 2nd Edition,, Princeton Unversity Press, (2013). Google Scholar

show all references

References:
[1]

F. Englert and R. Brout, Broken symmetry and the mass of gauge vector mesons,, Physical Review Letters, 13 (1964), 321. doi: 10.1103/PhysRevLett.13.321. Google Scholar

[2]

D. Griffiths, Introduction to Elementary Particles,, Wiley-Vch, (2008). doi: 10.1002/9783527618460. Google Scholar

[3]

G. Guralnik, C. R. Hagen and T. W. B. Kibble, Global conservation laws and massless particles,, Physical Review Letters, 13 (1964), 585. doi: 10.1103/PhysRevLett.13.585. Google Scholar

[4]

F. Halzen and A. D. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics,, John Wiley and Sons, (1984). Google Scholar

[5]

P. W. Higgs, Broken symmetries and the masses of gauge bosons,, Physical Review Letters, 13 (1964), 508. doi: 10.1103/PhysRevLett.13.508. Google Scholar

[6]

M. Kaku, Quantum Field Theory, A Modern Introduction,, Oxford University Press, (1993). Google Scholar

[7]

G. Kane, Modern Elementary Particle Physics,, vol. 2, (1987). Google Scholar

[8]

T. Ma and S. Wang, Bifurcation Theory and Applications,, vol. 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, (2005). doi: 10.1142/9789812701152. Google Scholar

[9]

_______, Duality theory of strong interaction,, Electronic Journal of Theoretical Physics, (2014), 101. Google Scholar

[10]

_______, Duality theory of weak interaction,, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, (2012). Google Scholar

[11]

_______, Unified field theory and principle of representation invariance,, arXiv:1212.4893; version 1 appeared in Applied Mathematics and Optimization, 69 (2014), 359. doi: 10.1007/s00245-013-9226-0. Google Scholar

[12]

_______, Gravitational field equations and theory of dark matter and dark energy,, Discrete and Continuous Dynamical Systems, 34 (2014), 335. Google Scholar

[13]

_______, Weakton model of elementary particles and decay mechanisms,, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, (2013). Google Scholar

[14]

Y. Nambu, Quasi-particles and gauge invariance in the theory of superconductivity,, Phys. Rev., 117 (1960), 648. doi: 10.1103/PhysRev.117.648. Google Scholar

[15]

Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I,, Phys. Rev., 122 (1961), 345. doi: 10.1103/PhysRev.122.345. Google Scholar

[16]

_______, Dynamical model of elementary particles based on an analogy with superconductivity. II,, Phys. Rev., 124 (1961), 246. Google Scholar

[17]

C. Quigg, Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, 2nd Edition,, Princeton Unversity Press, (2013). Google Scholar

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