Unified field equations coupling four forces and principle of interaction dynamics

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

Unified field equations coupling four forces and principle of interaction dynamics

Tian Ma ^1, and Shouhong Wang ^2,

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

Abstract
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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.

Keywords: unified field equations, dual particle fields, solar neutrino problem, Higgs mechanism, dark energy, short-range nature of strong and weak interactions, baryon asymmetry., Principle of interaction dynamics (PID), fundamental interactions, asymptotic freedom, quark confinement, principle of representation invariance, gauge symmetry breaking, dark matter.

Mathematics Subject Classification: 81T13, 83E9.

Citation: Tian Ma, Shouhong Wang. Unified field equations coupling four forces and principle of interaction dynamics. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1103-1138. doi: 10.3934/dcds.2015.35.1103

References:

[1]	F. Englert and R. Brout, Broken symmetry and the mass of gauge vector mesons, Physical Review Letters, 13 (1964), 321-323. doi: 10.1103/PhysRevLett.13.321.
[2]	D. Griffiths, Introduction to Elementary Particles, Wiley-Vch, 2008. doi: 10.1002/9783527618460.
[3]	G. Guralnik, C. R. Hagen and T. W. B. Kibble, Global conservation laws and massless particles, Physical Review Letters, 13 (1964), 585-587. doi: 10.1103/PhysRevLett.13.585.
[4]	F. Halzen and A. D. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics, John Wiley and Sons, New York, NY, 1984.
[5]	P. W. Higgs, Broken symmetries and the masses of gauge bosons, Physical Review Letters, 13 (1964), 508-509. doi: 10.1103/PhysRevLett.13.508.
[6]	M. Kaku, Quantum Field Theory, A Modern Introduction, Oxford University Press, 1993.
[7]	G. Kane, Modern Elementary Particle Physics, vol. 2, Addison-Wesley Reading, 1987.
[8]	T. Ma and S. Wang, Bifurcation Theory and Applications, vol. 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. doi: 10.1142/9789812701152.
[9]	_______, Duality theory of strong interaction, Electronic Journal of Theoretical Physics, 11:31(2014), 101-124.
[10]	_______, Duality theory of weak interaction, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, #1302: http://www.indiana.edu/~iscam/preprint/1302.pdf, (2012).
[11]	_______, Unified field theory and principle of representation invariance, arXiv:1212.4893; version 1 appeared in Applied Mathematics and Optimization, 69 (2014), 359-392. doi: 10.1007/s00245-013-9226-0.
[12]	_______, Gravitational field equations and theory of dark matter and dark energy, Discrete and Continuous Dynamical Systems, Ser. A, 34 (2014), 335-366; see also arXiv:1206.5078v2.
[13]	_______, Weakton model of elementary particles and decay mechanisms, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, #1304: http://www.indiana.edu/~iscam/preprint/1304.pdf, (May 30, 2013).
[14]	Y. Nambu, Quasi-particles and gauge invariance in the theory of superconductivity, Phys. Rev., 117 (1960), 648-663. doi: 10.1103/PhysRev.117.648.
[15]	Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I, Phys. Rev., 122 (1961), 345-358. doi: 10.1103/PhysRev.122.345.
[16]	_______, Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev., 124 (1961), 246-254.
[17]	C. Quigg, Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, 2nd Edition, Princeton Unversity Press, 2013.

show all references

References:

[1]	F. Englert and R. Brout, Broken symmetry and the mass of gauge vector mesons, Physical Review Letters, 13 (1964), 321-323. doi: 10.1103/PhysRevLett.13.321.
[2]	D. Griffiths, Introduction to Elementary Particles, Wiley-Vch, 2008. doi: 10.1002/9783527618460.
[3]	G. Guralnik, C. R. Hagen and T. W. B. Kibble, Global conservation laws and massless particles, Physical Review Letters, 13 (1964), 585-587. doi: 10.1103/PhysRevLett.13.585.
[4]	F. Halzen and A. D. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics, John Wiley and Sons, New York, NY, 1984.
[5]	P. W. Higgs, Broken symmetries and the masses of gauge bosons, Physical Review Letters, 13 (1964), 508-509. doi: 10.1103/PhysRevLett.13.508.
[6]	M. Kaku, Quantum Field Theory, A Modern Introduction, Oxford University Press, 1993.
[7]	G. Kane, Modern Elementary Particle Physics, vol. 2, Addison-Wesley Reading, 1987.
[8]	T. Ma and S. Wang, Bifurcation Theory and Applications, vol. 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. doi: 10.1142/9789812701152.
[9]	_______, Duality theory of strong interaction, Electronic Journal of Theoretical Physics, 11:31(2014), 101-124.
[10]	_______, Duality theory of weak interaction, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, #1302: http://www.indiana.edu/~iscam/preprint/1302.pdf, (2012).
[11]	_______, Unified field theory and principle of representation invariance, arXiv:1212.4893; version 1 appeared in Applied Mathematics and Optimization, 69 (2014), 359-392. doi: 10.1007/s00245-013-9226-0.
[12]	_______, Gravitational field equations and theory of dark matter and dark energy, Discrete and Continuous Dynamical Systems, Ser. A, 34 (2014), 335-366; see also arXiv:1206.5078v2.
[13]	_______, Weakton model of elementary particles and decay mechanisms, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, #1304: http://www.indiana.edu/~iscam/preprint/1304.pdf, (May 30, 2013).
[14]	Y. Nambu, Quasi-particles and gauge invariance in the theory of superconductivity, Phys. Rev., 117 (1960), 648-663. doi: 10.1103/PhysRev.117.648.
[15]	Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I, Phys. Rev., 122 (1961), 345-358. doi: 10.1103/PhysRev.122.345.
[16]	_______, Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev., 124 (1961), 246-254.
[17]	C. Quigg, Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, 2nd Edition, Princeton Unversity Press, 2013.

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