Maxwell’s equations in four-dimensional notation and the classical magnetic monopoles |
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| Institution: | 1. Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania;2. Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania;3. Department of Neurology, University of Pennsylvania, Philadelphia, Pennsylvania;4. Department of Psychiatry, University of Pennsylvania, Philadelphia, Pennsylvania;1. Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA;2. Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada;3. Fermilab, Batavia, IL 60510, USA;4. Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506, USA;5. Physics Department, Technion—Israel Institute of Technology, Haifa 32000, Israel;6. Department of Physics, LEPP, Cornell University, Ithaca, NY 14853, USA;7. Department of Physics, Korea University, Seoul 136-713, Republic of Korea;1. Department of Psychology, University of Pittsburgh, Pittsburgh, PA 15260, United States;2. Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Mellon University, Pittsburgh, PA 15213, United States;1. Department of Physiology and Cell Biology, School of Medicine, University of Nevada, Reno, Nevada;2. Division of Biological Sciences, Wonkwang University, Iksan, Chonbuk, Korea;3. Department of Physiology, Wonkwang Digestive Disease Research Institute and Institute of Wonkwang Medical Science, School of Medicine, Wonkwang University, Iksan, Chonbuk, Korea;4. Division of Gastroenterology and Hepatology, Stanford University School of Medicine, Stanford, California;1. Physik-Department, Technische Universität München, 85748 Garching, Germany;2. Institut für Kernphysik, Universität zu Köln, 50937 Köln, Germany;3. College of Physics & Engineering Science, University of Guelph, 50 Stone Road East Guelph, Ontario N1G 2W1, Canada;4. Physical Sciences Division, TRIUMF, Vancouver, British Columbia, V6T 2A3, Canada;5. GSI Helmholtzzentrum für Schwerionenforschung, D-64291 Darmstadt, Germany;6. Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain;7. Department of Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;8. Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA;9. Departamento de Física Teórica, Universidad Autónoma de Madrid, E-28049 Madrid, Spain;10. IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France;11. Institut für Kernphysik, Technische Universität Darmstadt, Germany;12. ISOLDE, CERN, CH-1211, Geneva, Switzerland;13. Dipartimento di Fisica, Università degli Studi di Milano and INFN Sez. Milano, Milano I-20133, Italy;14. KU Leuven, Instituut voor Kern- en Stralingsfysica, 3001 Leuven, Belgium;15. Normandie Univ, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, 14000 Caen, France;p. Department of Physics, University of Oslo, N-0316 Oslo, Norway;q. Department of Physics, Ludwig Maximilian Universität München, 85748 Garching, Germany;r. Department of Physics, University of Jyväskylä, P.O. Box 35, FI-40014 Jyväskylä, Finland;s. Paul Scherrer Institut, Villigen, Switzerland;t. School of Computing, Engineering, and Physical Sciences, University of the West of Scotland, Paisley PA1 2BE, UK;u. Department of Physics, University of York, YO10 5DD, United Kingdom |
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| Abstract: | It is shown that, on account of the commutability of the order of derivation of the electromagnetic 4-potential, the first pair of Maxwell equations, when written in a four dimensional notation, is incompatible with the existence of the classical magnetic monopole. It is hypothesized that the appearance in the past of magnetic monopoles could be accepted only if, in exceptional occurrences, it came to be locally lacking the space homogeneity and isotropy on which the commutability of space derivatives is based. The situation is more complex for massive cosmological monopoles. |
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| Keywords: | Classical magnetic monopole Earthquake Demagnetization Non-commutative geometry |
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