A unified model with a generalized gauge symmetry and its cosmological implications

  • A unified model is based on a generalized gauge symmetry with groups [SU3c]color × (SU2× U1) × [U1b× U1l]. It implies that all interactions should preserve conservation laws of baryon number, lepton number, and electric charge, etc. The baryonic U1b, leptonic U1l and color SU3c gauge transformations are generalized to involve non-integrable phase factors. One has gauge invariant fourth-order equations for massless gauge fields, which leads to linear potentials in the [U1b× U1l] and color [SU3c] sectors. We discuss possible cosmological implications of the new baryonic gauge field. It can produce a very small constant repulsive force between two baryon galaxies (or between two anti-baryon galaxies), where the baryon force can overcome the gravitational force at very large distances and leads to an accelerated cosmic expansion. Based on conservation laws in the unified model, we discuss a simple rotating dumbbell universe with equal amounts of matter and anti-matter, which may be pictured as two gigantic rotating clusters of galaxies. Within the gigantic baryonic cluster, a galaxy will have an approximately linearly accelerated expansion due to the effective force of constant density of all baryonic matter. The same expansion happens in the gigantic anti-baryonic cluster. Physical implications of the generalized gauge symmetry on charmonium confining potentials due to new SU3c field equations, frequency shift of distant supernovae Ia and their experimental tests are discussed.
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  • [1] Hsu J P. Mod. Phys. Letts. A, 2011, 26: 1707. arXiv: 1106.2121[2] Hsu, J P. Chin. Phys. C, 2012 36(5): 403[3] Noether E, Goett. Nachr., 1918, 235. In German[4] HUANG K. Quarks, Leptons and Gauge Field. Singapore: World Scientific, 1982. 103-121, 241-242[5] Salam A and Ward J C, Phys. Letters, 1964, 13: 168[6] WU T-Y, Pauchy Hwang W-Y. Relativistic Quantum Mechanics and Quantum Fields. Singapore: World Scientific, 1991. Chpts. 12, 13 and 14[7] Marshak R E. Conceptual Foundations of Modern Particle Physics. Singapore: World Scientific, 1993. Ch. 2[8] Hsu J P. Euro. Phys. J. Plus., 2014, 129: 108[9] Hsu J P. Mod. Phys. Letts. A, 2014, 29: 1450031[10] Hsu J P. Phys. Rev. Lett., 1976, 36: 1515[11] Peebles P J E and Ratra B. Rev. Mod. Phys., 2003 75: 559 and references therein[12] Dyson F. Missed Opportunities. In: Hsu J P, Fine D. 100 Years of Gravity and Accelerated Frames, The Deepest Insights of Einstein and Yang-Mills. Singapore, World Scientific, 2005. 348[13] Hsu J P, Hsu L. Space-Time Symmetry and Quantum Yang-Mills Gravity. Singapore: World Scientific, 2013. 212-215, 225[14] Vlasov N A. Soviet Astronomy, 1965, 8: 715[15] Hsu J P. Int. J. Modern Phys. A, 2006, 21: 5119[16] Hsu J P, Kim S H. Euro. Phys. J. Plus, 2012, 127: 146[17] Gamba A, Marshak R E, Okubo S. Proc. Nat. Acad. Sci. U.S., 1959, 45: 881[18] Eichten E, Gottfried K, Kinoshita T, Kought J, Lane K D, YAN T-M. Phys. Rev. Lett., 1975, 34: 369[19] WANG Q, KUANG Y P. In: WU Y L, Hsu J P. Symposium on the Frontiers of Physics at Millennium, Singapore, World Scientific, 2001. 51-59, 344-354[20] Chou K C, WU Y L. Phys. Rev. D, 1996, 53: R3492-R3496[21] Weinberg S. The Quantum Theory of Fields Vol. 2. London: Cambridge Univ. Press, 1996. 152-157[22] de Wet J S. Math. Proc. of the Cambridge Phil. Soc., 1948, 44: 546[23] Pais A, Uhlenbeck G E. Phys. Rev., 1950, 79: 145[24] Bopp F. Ann. d. Physik, 1940, 38: 345[25] Takeno Y. Prog. Theore. Phys., 1961, 26: 304[26] Bender C M, Mannheim P D. Phys. Rev. Letters, 2008, 100: 110402[27] Mannheim P D. Found. Phys., 2007, 37: 532[28] Bender C M, TAN B. J. Phys. A, 2006, 39: 1945[29] Hsu J P. Mod. Phys. Letters, 2014, 29: 1450120; Erratum and Addendum, 2014 {ibid}[30] Lee T D, YANG C N. Conservation of Heavy Particles and Generalized Gauge Transformations. In: Hsu J P, Fine D. 100 Years of Gravity and Accelerated Frames, The Deepest Insights of Einstein and Yang-Mills, Singapore, World Scientific, 2005. 155. See also p. 504.[31] Hsu J P and NING Z H. Cosmic Lee-Yang Force, Dark Energy and Accelerated Wu-Doppler Effect. In: Nester J M, CHEN C M, Hsu J P. Proc. of the VII Asia-Pacific Int. Conf. on Gravitation and Astrophysics, Singapore, World Scientific, 2007. 79[32] Olive K A et al (Partick Data Group). Chin. Phys. C, 2014, 38: 090001[33] Rothman T, Sudarshan, E C G. Doubt and Certainty. Reading, Mass., Helix Books, 1998. 214-264
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Jong-Ping Hsu and Kazuo O. Cottrell. A unified model with a generalized gauge symmetry and its cosmological implications[J]. Chinese Physics C, 2015, 39(10): 105101. doi: 10.1088/1674-1137/39/10/105101
Jong-Ping Hsu and Kazuo O. Cottrell. A unified model with a generalized gauge symmetry and its cosmological implications[J]. Chinese Physics C, 2015, 39(10): 105101.  doi: 10.1088/1674-1137/39/10/105101 shu
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Received: 2015-01-20
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A unified model with a generalized gauge symmetry and its cosmological implications

    Corresponding author: Jong-Ping Hsu,
    Corresponding author: Kazuo O. Cottrell,

Abstract: A unified model is based on a generalized gauge symmetry with groups [SU3c]color × (SU2× U1) × [U1b× U1l]. It implies that all interactions should preserve conservation laws of baryon number, lepton number, and electric charge, etc. The baryonic U1b, leptonic U1l and color SU3c gauge transformations are generalized to involve non-integrable phase factors. One has gauge invariant fourth-order equations for massless gauge fields, which leads to linear potentials in the [U1b× U1l] and color [SU3c] sectors. We discuss possible cosmological implications of the new baryonic gauge field. It can produce a very small constant repulsive force between two baryon galaxies (or between two anti-baryon galaxies), where the baryon force can overcome the gravitational force at very large distances and leads to an accelerated cosmic expansion. Based on conservation laws in the unified model, we discuss a simple rotating dumbbell universe with equal amounts of matter and anti-matter, which may be pictured as two gigantic rotating clusters of galaxies. Within the gigantic baryonic cluster, a galaxy will have an approximately linearly accelerated expansion due to the effective force of constant density of all baryonic matter. The same expansion happens in the gigantic anti-baryonic cluster. Physical implications of the generalized gauge symmetry on charmonium confining potentials due to new SU3c field equations, frequency shift of distant supernovae Ia and their experimental tests are discussed.

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