Yang-Mills Field from Quaternion Space Geometry, and its Klein-Gordon Representation

POSTER

Abstract

Analysis of covariant derivatives of vectors in quaternion (Q-) spaces performed using Q-unit spinor-splitting technique and use of SL(2C)-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM) field principle characteristics. In particular, it is shown that Q-connexion (with quaternion non-metricity) and related curvature of 4 dimensional (4D) space-times with 3D Q-space sections are formally equivalent to respectively YM-field potential and strength, traditionally emerging from the minimal action assumption. Plausible links between YM field equation and Klein-Gordon equation, in particular via its known isomorphism with Duffin-Kemmer equation, are also discussed.

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Authors

  • Joshua Lusk

    University of New Mexico, Gallup Campus, Sciprint.org, Institute of Gravitation and Cosmology, Moscow, Russia, CSU Long Beach, California State University - East Bay, LLNL, UC Santa Cruz, University of California, Berkeley, Loma Linda Medical University, Northern Illinois University, Santa Cruz Institute for Particle Physics, Dr, Pr, California State University Long Beach, California Polytechnic State University, Department of Physics, California State University, Fresno, NPS, UC-Davis, University of California-Davis, University of California Riverside, Rutgers University, Pomona College, Department of Physics, Imperial College London, Materials Research Laboratory, UC Santa Barbara, Naval Postgraduate School, Whittier College, Cardiff University, Cardiff, Wales - Cardiff School of Biosciences, University of California, Davis - Electrical and Computer Engineering, University of California, Davis - Neurosurgery, Materials Department, University of California, Santa Barbara, CA 93106-5050, Queen's University, Belfast, Rutherford Appleton Laboratory, Technical University of Darmstadt, University of York, University of California, Los Angeles, Kohat University of Science and Technology, Lawrence Livermore National Laboratory, Imperial College, The Blackett Laboratory, University of Strathclyde, University of Oxford, UC Berkeley, UC Berkeley, SLAC, Gesellschaft f\"ur Schwerionenforschung GSI, University of Washington, Seattle, LLNL and XIA LLC, University of Graz, University of California, Davis, Naval Surface Warfare Center-Indian Head Division

  • Joshua Lusk

    University of New Mexico, Gallup Campus, Sciprint.org, Institute of Gravitation and Cosmology, Moscow, Russia, CSU Long Beach, California State University - East Bay, LLNL, UC Santa Cruz, University of California, Berkeley, Loma Linda Medical University, Northern Illinois University, Santa Cruz Institute for Particle Physics, Dr, Pr, California State University Long Beach, California Polytechnic State University, Department of Physics, California State University, Fresno, NPS, UC-Davis, University of California-Davis, University of California Riverside, Rutgers University, Pomona College, Department of Physics, Imperial College London, Materials Research Laboratory, UC Santa Barbara, Naval Postgraduate School, Whittier College, Cardiff University, Cardiff, Wales - Cardiff School of Biosciences, University of California, Davis - Electrical and Computer Engineering, University of California, Davis - Neurosurgery, Materials Department, University of California, Santa Barbara, CA 93106-5050, Queen's University, Belfast, Rutherford Appleton Laboratory, Technical University of Darmstadt, University of York, University of California, Los Angeles, Kohat University of Science and Technology, Lawrence Livermore National Laboratory, Imperial College, The Blackett Laboratory, University of Strathclyde, University of Oxford, UC Berkeley, UC Berkeley, SLAC, Gesellschaft f\"ur Schwerionenforschung GSI, University of Washington, Seattle, LLNL and XIA LLC, University of Graz, University of California, Davis, Naval Surface Warfare Center-Indian Head Division

  • Joshua Lusk

    University of New Mexico, Gallup Campus, Sciprint.org, Institute of Gravitation and Cosmology, Moscow, Russia, CSU Long Beach, California State University - East Bay, LLNL, UC Santa Cruz, University of California, Berkeley, Loma Linda Medical University, Northern Illinois University, Santa Cruz Institute for Particle Physics, Dr, Pr, California State University Long Beach, California Polytechnic State University, Department of Physics, California State University, Fresno, NPS, UC-Davis, University of California-Davis, University of California Riverside, Rutgers University, Pomona College, Department of Physics, Imperial College London, Materials Research Laboratory, UC Santa Barbara, Naval Postgraduate School, Whittier College, Cardiff University, Cardiff, Wales - Cardiff School of Biosciences, University of California, Davis - Electrical and Computer Engineering, University of California, Davis - Neurosurgery, Materials Department, University of California, Santa Barbara, CA 93106-5050, Queen's University, Belfast, Rutherford Appleton Laboratory, Technical University of Darmstadt, University of York, University of California, Los Angeles, Kohat University of Science and Technology, Lawrence Livermore National Laboratory, Imperial College, The Blackett Laboratory, University of Strathclyde, University of Oxford, UC Berkeley, UC Berkeley, SLAC, Gesellschaft f\"ur Schwerionenforschung GSI, University of Washington, Seattle, LLNL and XIA LLC, University of Graz, University of California, Davis, Naval Surface Warfare Center-Indian Head Division