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Kaluza, Klein, confinement, and nuclear forces

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Abstract

The nonsymmetric Kaluza-Klein and Jordan-Thiry theories are reviewed as interesting propositions of physics in higher dimensions. It is shown how a dielectric model of confinement can be derived from “interference effects” in these theories. It is postulated that the old puzzle of nuclear physics,σ-particles, can be connected to the skewon fieldg [μv] and the scalar field Ψ in the nonsymmetric Jordan-Thiry theory. Similarities are pointed out between the nonsymmetric Jordan-Thiry Lagrangian in the flat space limit and the soliton bag model Lagrangian. Finally the nonsymmetric Jordan-Thiry Lagrangian is proposed as the bosonic part of the strong interaction Lagrangian.

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References

  1. Adkins, G. S., Nappi, R. C., and Witten, E. (1982). Static properties of nucleons in the Skyrme model, inProceedings of the Third Annual JCTP Summer Workshop on Particle Physics, p. 170, Miramare-Trieste.

  2. Brown, G. E. (1972). Elementary-particle models of the two-nucleon force, inThe Two-Body Force in Nuclei, S. M. Austin and G. M. Crawley, eds., p. 29. Plenum Press, New York.

  3. Bryan, R. A., and Scott, B. L. (1964). Nucleon-nucleon scattering from one-boson exchange potentials,Physical Review,135, B434.

  4. Cho, Y. (1975). Higher dimensional unification of gravitation and gauge theories,Journal of Mathematical Physics,16, 2029.

  5. Detar, C. E., and Donoghue, J. E. (1983). Bag model of hadrons, inAnnual Review of Nuclear and Particle Science,33, 235.

  6. Einstein, A. (1905). Zur elektrodynamik bewegter Körper,Annalen der Physik,17, 891.

  7. Einstein, A. (1941).Revista Universidad Nacional Tucumán,2, 11.

  8. Einstein, A. (1945). A generalization of the relativistic theory of gravitation,Annals of Mathematics,46, 578.

  9. Einstein, A. (1951).The Meaning of Relativity, 5th ed. Methuen and Co., London.

  10. Einstein, A., and Kaufman, B. (1954).Annals of Mathematics,59, 230.

  11. Einstein, A., and Pauli, W. (1943).Annals of Mathematics,44, 131.

  12. Einstein, A., and Strauss, É. G. (1946). A generalization of the relativistic theory of gravitation II,Annals of Mathematics,47, 731.

  13. Friedberg, R., and Lee, T. D. (1978). Quantum chronomodynamics and the soliton models of hadrons,Physical Review D,18, 2623.

  14. Goldflam, R., and Wilets, L. (1982). Soliton bag model,Physical Review D,25, 1951.

  15. Hubert, D. (1916).Göttingen Nachrichten,12.

  16. Isham, C. J., Salam, A., and Strathdee, J. (1971). f-Dominance of gravity,Physical Review D,3, 867.

  17. Jordan, P. (1955).Schwerkraft und Weltall. Vieweg, Braunschweig.

  18. Kalinowski, M. W. (1981a). PC nonconservation and dipole electric moment of fermion in the Klein-Kaluza theory,Acta Physica Austriaca,53, 229.

  19. Kalinowski, M. W. (1981b). Gauge fields with torsion,International Journal of Theoretical Physics,20, 563.

  20. Kalinowski, M. W. (1982a). Rarita-Schwinger fields in nonabelian Klein-Kaluza theories,Journal of Physics A,15, 2441.

  21. Kalinoswki, M. W. (1982b). Spontaneous symmetry breaking and Higgs' mechanism in the nonsymmetric Jordan-Thiry theory, University of Toronto Report (to appear inForschnitte der Physik).

  22. Kalinowski, M. W. (1982c). PC nonconservation and a dipole electric moment of fermion in the nonsymmetric Kaluza-Klein theory, University of Toronto Report.

  23. Kalinowski, M. W. (1982d). Spinor fields in the nonsymmetric-nonabelian Kaluza-Klein theory, University of Toronto Report.

  24. Kalinowski, M. W. (1982e). An Einstein-Cartan-Moffat theory,Physical Review D,26, 3419.

  25. Kalinowski, M. W. (1983a). Vanishing of the cosmological constant in nonabelian Klein-Kaluza theories,International Journal of Theoretical Physics,22, 385.

  26. Kalinowski, M. W. (1983b). 3/2 spinor field in the Klein-Kaluza theory,Acta Physica Austriaca,55, 167.

  27. Kalinowski, M. W. (1983c). The nonsymetric Kaluza-Klein theory,Journal of Mathematical Physics,24, 1835.

  28. Kalinowski, M. W. (1983d). On the nonsymmetric Jordan-Thiry theory,Canadian Journal of Physics,61, 844.

  29. Kalinowski, M. W. (1983e). The nonsymmetric-nonabelian Kaluza-Klein theory.Journal of Physics A,16, 1669.

  30. Kalinowski, M. W. (1983f). Spontaneous symmetry breaking and Higgs' mechanism in the nonsymmetric Kaluza-Klein theory,Annals of Physics,148, 214.

  31. Kalinowski, M. W. (1984a). Spinor fields in nonabelian Klein-Kaluza theories,International Journal of Theoretical Physics,23, 131.

  32. Kalinowski, M. W. (1984b). The nonsymmetric-nonabelian Jordan-Thiry theory,Il Nuovo Cimento,LXXXA, 47.

  33. Kalinowski, M. W. (1984c). Material sources in the nonsymmetric Kaiuza-Klein theory,Journal of Mathematical Physics,25, 1045.

  34. Kalinowski, M. W., and Kunstatter, G. (1984). Spherically symmetric solution in the nonsymmetric Kaiuza-Klein theory,Journal of Mathematical Physics,25, 117.

  35. Kalinowski, M. W., and Mann, R. B. (1983). Linear approximation in the nonsymmetric Jordan-Thiry theory, University of Toronto Report (to appear inNuovo Cimento).

  36. Kalinowski, M. W., and Mann, R. B. (1984). Linear approximation in the nonsymmetric Kaluza-Klein theory,Classical and Quantum Gravity,1, 157.

  37. Kaluza, T. (1921). Zum Unitätsproblem der Physik,Sitzungsberichte Preussische Akademie der Wissenschaften,1921, 966.

  38. Kaufman, B. (1955).Annals of Mathematics,62, 128.

  39. Kaufman, B. (1956). Mathematical structure of the nonsymmetric field theory,Helvetica Physica Acta Supplementum,1956, 227.

  40. Kerner, R. (1968). Generalization of Kaluza-Klein theory for an arbitrary nonabelian gauge group,Annales de l'Institut Henry Poincaré, Section A: Physiqué Theorique,IX, 143.

  41. Klein, O. (1926).Zeitschrift für Physik,37, 895.

  42. Klein, O. (1939). On the theory of charged fields, inNew Theories in Physics (Conference organized in collaboration with the International Union of Physics and the Polish Cooperation Committee, Warsaw, May 30–June 3, 1938), p. 77. Paris, 1939.

  43. Kogut, J. B. (1983). Dielectric model of confinement, in Lattice Gauge Theory Approach to Quantum Chromodynamics,Reviews of Modern Physics,55, 182.

  44. Kopczyński, W. (1980). A fibre bundle description of coupled gravitational and gauge fields, inDifferential Geometrical Methods in Mathematical Physics, p. 462. Springer, Berlin.

  45. Kramer, D., Stephani, H., MacCallum, M., and Herlt, E. (1980).Exact Solutions of Einstein's Field Equations. Cambridge University Press, Cambridge.

  46. Kunstatter, G., Moffat, J. W., and Malzan, J. (1983). Geometrical interpretation of a generalized theory of gravitation,Journal of Mathematical Physics,24, 886.

  47. Lee, T. D. (1979). Feynman rules of quantum chromodynamics inside a hadron,Physical Review D,19, 1802.

  48. Lee, T. D. (1981).Particle Physics and Introduction to Field Theory. Harwood, New York.

  49. Lehman, H., and Wu, T. T. (1983). Classical Models of Confinement, Preprint DESY83-086.

  50. Levi-Civita (1917).Atti Accademia Nazionale dei Luncei Classe de Scienze Fisichi, Matematiche e Naturali Memorie,26, 311.

  51. Lichnerowicz, A. (1939).Sur certains problems globaux relatifs au systeme des equations d'Einstein. Hermann, Paris.

  52. Lichnerowicz, A. (1955).Théorie relativistes de la gravitation et de l'électromagnetisme. Masson, Paris.

  53. Mann, R. B. (1985). Exact solution of an algebraically extended Kaluza-Klein theory,Journal of Mathematical Physics,26, 2308.

  54. Mann, R. B., and Moffat, J. W. (1982a). Field redefinition of a string Lagrangian in a generalized theory of gravitation,Physical Review D,25, 3410.

  55. Mann, R. B., and Moffat, J. W. (1982b). Ghost properties of generalized theories of gravitation,Physical Review D,26, 1858.

  56. Mau Vinh, R. (1978). Nucleon-nucleon potentials and theoretical developments. An overview of the nucleon-nucleon interaction, inNucleon-Nucleon Interactions, p. 140, AIP Conference Proceedings, No. 41.

  57. Mihich, L. (1983). Static and stationary solutions of Moffat's theory of gravitation: Generalization of some classes of the Einstein-Maxwell fields,II Nuovo Cimento,LXXB, 115.

  58. Moffat, J. W. (1982). Generalized theory of gravitation and its physical consequences, inProceedings of the VII International School of Gravitation and Cosmology, Erice, Sicilly, V. de Sabbata, ed., p. 127. World Scientific Publishing Co., Singapore.

  59. Rho, M. (1984). Pion interactions within nuclei, inAnnual Review of Nuclear and Particle Science, Vol. 14, p. 54.

  60. Skyrme, R. H. T. (1961).Proceedings of the Royal Society, Series A,260, 127.

  61. Tafel, J., and Trautman, A. (1983). Can poles change color?,Journal of Mathematical Physics,24, 1087.

  62. Thirring, W. (1972). Five dimensional theories and CP violation,Acta Physica Austriaca Supplementum,IX, 256.

  63. Thiry, Y. (1951a).Étude mathématique d'équations d'une théorie unitaire à quinze variables de champ. Gautiers-Villars, Paris.

  64. Thiry, Y. (1951).Journal de Mathematics Pures et Appliquées,30, 275.

  65. Thomas, A. W. (1982). Chiral symmetry and the bag model: A new starting point for nuclear physics, TH. 3368-CERN TRI-PP-82-29.

  66. Weder, R. (1982). Absence of stationary solutions to Einstein-Yang-Mills equations,Physical Review D,25, 2515.

  67. Witten, E. (1981). Search for a realistic Kaluza-Klein Theory,Nuclear Physics B,186, 412.

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On leave of absence from the Institute of Philosophy and Sociology of the Polish Academy of Science, 00-330 Warsaw, Poland.

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Kalinowski, M.W. Kaluza, Klein, confinement, and nuclear forces. Int J Theor Phys 25, 327–345 (1986). https://doi.org/10.1007/BF00670763

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Keywords

  • Soliton
  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Strong Interaction