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Relativistic pendulum and invariant curves
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 
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. 
[2] 
D. Griffiths, Introduction to Elementary Particles,, WileyVch, (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. 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, (1984). 
[5] 
P. W. Higgs, Broken symmetries and the masses of gauge bosons,, Physical Review Letters, 13 (1964), 508. 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, (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, (2005). doi: 10.1142/9789812701152. 
[9] 
_______, Duality theory of strong interaction,, Electronic Journal of Theoretical Physics, (2014), 101. 
[10] 
_______, Duality theory of weak interaction,, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, (2012). 
[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/s0024501392260. 
[12] 
_______, Gravitational field equations and theory of dark matter and dark energy,, Discrete and Continuous Dynamical Systems, 34 (2014), 335. 
[13] 
_______, Weakton model of elementary particles and decay mechanisms,, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, (2013). 
[14] 
Y. Nambu, Quasiparticles and gauge invariance in the theory of superconductivity,, Phys. Rev., 117 (1960), 648. doi: 10.1103/PhysRev.117.648. 
[15] 
Y. Nambu and G. JonaLasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I,, Phys. Rev., 122 (1961), 345. doi: 10.1103/PhysRev.122.345. 
[16] 
_______, Dynamical model of elementary particles based on an analogy with superconductivity. II,, Phys. Rev., 124 (1961), 246. 
[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. doi: 10.1103/PhysRevLett.13.321. 
[2] 
D. Griffiths, Introduction to Elementary Particles,, WileyVch, (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. 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, (1984). 
[5] 
P. W. Higgs, Broken symmetries and the masses of gauge bosons,, Physical Review Letters, 13 (1964), 508. 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, (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, (2005). doi: 10.1142/9789812701152. 
[9] 
_______, Duality theory of strong interaction,, Electronic Journal of Theoretical Physics, (2014), 101. 
[10] 
_______, Duality theory of weak interaction,, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, (2012). 
[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/s0024501392260. 
[12] 
_______, Gravitational field equations and theory of dark matter and dark energy,, Discrete and Continuous Dynamical Systems, 34 (2014), 335. 
[13] 
_______, Weakton model of elementary particles and decay mechanisms,, Indiana University Institute for Scientific Computing and Applied Mathematics Preprint Series, (2013). 
[14] 
Y. Nambu, Quasiparticles and gauge invariance in the theory of superconductivity,, Phys. Rev., 117 (1960), 648. doi: 10.1103/PhysRev.117.648. 
[15] 
Y. Nambu and G. JonaLasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I,, Phys. Rev., 122 (1961), 345. doi: 10.1103/PhysRev.122.345. 
[16] 
_______, Dynamical model of elementary particles based on an analogy with superconductivity. II,, Phys. Rev., 124 (1961), 246. 
[17] 
C. Quigg, Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, 2nd Edition,, Princeton Unversity Press, (2013). 
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