Abstract
This paper is devoted to an (n+4)-dimensional unification of NGT (nonsymmetric gravitation theory) and Yang-Mills theory in a Jordan-Thiry manner. We find “interference effects” between gravitational and Yang-Mills fields which appear to be due to the skew-symmetric part of the metric on the (n+4)-dimensional manifold (nonsymmetrically metrized principal fiber bundle). Our unification, called the nonsymmetric-non-Abelian Jordan-Thiry theory, becomes classical if the skew-symmetric part of the metric is zero. We find the Yang-Mills field Lagrangian up to the second order of approximation inh μν =g μν −η μν . We also deal with the Lagrangian for the scalar field (connected to the “gravitational constant”). We consider the spin content of the theory and a relationship between the cosmological constant and the coupling constant between the skewon field and the gauge field in the first order of approximation. We show how to derive a dielectric model of a confinement from “interference effects” in these theories. We underline some similarities between the nonsymmetric Jordan-Thiry Lagrangian in the flat space limit and the soliton bag model Lagrangian.
Similar content being viewed by others
References
Kaluza, T. (1921). Zum Unitätsproblem der Physik,Sitzgungsberichte der Preussichen Akademic der Wissenschaften,1921, 966.
Klein, O. (1926).Zeitschrift der Physik,37, 895; Klein, O. (1939). On the theory of charged fields, inNew theories in Physics (Conference Organized in Collaboration with International Union of Physics and the Polish Co-operation Committee, Warsaw, May 30–June 3, 1938), Paris, p. 77.
Einstein, A. (1951).The Meaning of Relativity, AppendixII, 5th ed., rev., Methuen, London, p. 127; Jakubowicz, A., and Klekowska, J. (1969). The necessary and sufficient condition for the existence of the unique connection of the two-dimensional generalized Riemannian space,Tensor N, S.,20, 72; Chung, K. T., and Lee, Y. J. (1988).International Journal of Theoretical Physics,27, 1083; Chung, K. T., and Hwang, H. J. (1988).International Journal of Theoretical Physics,27, 1105; Shavokhina, N. S. (1986). Nonsymmetric metric in nonlinear field theory, Preprint of the JINR, P2-86-685, Dubna.
Kaufman, B. (1956). Mathematical structure of the nonsymmetric field theory,Helvetica Physica Acta Supplement,1956, 227; Chung, K. T. (1983). Some recurrence relations for Einstein's connection for 2-dimensional unified theory of relativity,Acta Mathematica Hungarica,41(1–2), 47.
Einstein, A., and Kaufman, B. (1954).Annals of Mathematics,59, 230; Kaufman, B. (1945).Annals of Mathematics,46, 578.
Einstein, A. (1945).Annals of Mathematics,46, 578; Einstein, A., and Strauss, E. G. (1946).Annals of Mathematics,47, 731.
Kerner, T. (1968).Annales de l'Institut Henri Poincaré,IX, 143.
Cho, Y. M. (1975).Journal of Mathematical Physics 16, 2029; Cho, Y. M., and Freund, P. G. O. (1975).Physical Review D,12, 1711.
Kopczyński, W. (1980). A fibre bundle description of coupled gravitational and gauge fields, inDifferential Geometrical Methods in Mathematical Physics, Springer-Verlag, Berlin, p. 462.
Kalinowski, M. W. (1983).International journal of Theoretical Physics,22, 385.
Thirring, W. (1972). Five dimensional theories and CP violation,Acta Physica Austriaca Supplement IX,1972, 256.
Kalinowski, M. W. (1981). PC nonconservation and dipole electric moment of fermion in the Kaluza-Klein Theory,Acta Physica Austriaca,53, 229.
Kalinowki, M. W. (1984).International Journal of Theoretical Physics,23, 131.
Kalinowski, M. W. (1983). 2/3 spinor field in the Klein-Kaluza theory,Acta Physica Austriaca,55, 197.
Kalinowski, M. W. (1982).Journal of Physics A: Mathematical and General,15, 2441.144.
Kalinowski, M. W. (1981).International Journal of Theoretical Physics,20, 563.
Einstein, A. (1905).Annalen der Physik,17, 891.
Kalinowski, M. W. (1983).Journal of Mathematical Physics,24, 1835.
Kalinowski, M. W. (1983).Canadian Journal of Physics,61, 844.
Jordan, P. (1955).Shwerkraft und Weltal, Vieweg Verlag, Braunschweig.
Thirry, Y. (1951).Étude matématique de equations d'une theorie unitare a quinze variables de champ, Gautiers-Villars.
Lichnerowicz, A. (1955).Theoreie relativistes de la gravitation et de l'electromagnetisme, Masson, Paris.
Kalinowski, M. W. (1983).Journal of Physics A: Mathematical and General,16, 1669.
Kalinowski, M. W. (1984).Nuovo Cimenta 80A: 47.
Kalinowski, M. W. (1984).Journal of Mathematical Physics,25, 1045.
Kalinowski, M. W. (1983).Annals of Physics,148, 241.
Kalinowski, M. W. (1986).Fortschritte der Physik,34, 361.
Kalinowski, M. W., and Mann, R. B. (1984). Linear approximation in the nonsymmetric Kaluza-Klein theory,Classical and Quantum Gravity,1, 157.
Kalinowski, M. W., and Mann, R. B. (1986).Nuovo Cimenta,91B, 67.
Kalinowski, M. W., and Kunstatter, G. (1984).Journal of Mathematical Physics,25, 117.
Mann, R. B. (1985).Journal of Mathematical Physics,26, 2308.
Kalinowski, M. W. (1987).International Journal of Theoretical Physics,26, 21.
Kalinowski, M. W. (1987).International Journal of Theoretical Physics,26, 565.
Moffat, J. W. (1982). Generalized theory of gravitation and its physical consequences, inProceeding of the VII International School of Gravitation and Cosmology. Erice, V. de Sabbata, ed., World Scientific, Singapore, p. 127.
Kunstatter, G., Moffat, J. W., and Malzan, J. (1983).Journal of Mathematical Physics,24, 886.
Hilbert, D. (1916).Göttingen Nachrichten,12.
Levi-Civita, (1917).Atti Accademia Nazionale dei Lincei Classe di Scienze Fisichi, Matematiche e Naturali. Memorie, Thirry, Y. (1951).Journal de Mathématiques Pure et Appliquées,30, 275.
Lichnerowicz, A. (1939).Sur certains problems globaux relatifs au systeme des equations d'Einstein, Hermann, Paris.
Einstein, A., and Pauli, W. (1943).Annals of Mathematics,44, 131; Einstein, A. (1941).Revista Universidad Nacional Tucuman,2, 11.
Werder, R. (1982).Physical Review D,25, 2515; Bertnik, R., and McKinnon, J. (1988).Physical Review Letters,61, 141.
Kunstatter, G. (1984).Journal of Mathematical Physics,25, 2691.
Roseveare, N. T. (1982).Mercury's Perihelion: From Le Verrier to Einstein, Clarendon Press, Oxford.
Hlavaty, V. (1957).Geometry of Einstein's Unified Field Theory, Nordhoff-Verlag, Groningen; Tonnelat, M. A. (1966).Einstein's Unified Field Theory, Gordon and Breach, New York.
Hill, H. A., Bos, R. J., and Goode, P. R. (1983).Physical Review Letters,33, 709; Hill, H. A. (1984).International Journal of Theoretical Physics,23, 689; Gough, D. O. (1982).Nature,298, 334.
Moffat, J. W. (1983).Physical Review Letters,50, 709; Campbell, L., and Moffat, J. B. (1983).Astrophysical Journal,275, L77.
Moffat, J. W. (1982). The orbit of Icarus as a test of a theory of gravitation, University of Toronto preprint, May 1982; Campbell, L., McDow, J. C., Moffat, J. W., and Vincent, D. (1983).Nature,305, 508.
Moffat, J. W. (1984).Foundation of Physics,14, 1217; Moffat, J. W. (1981). Test of a theory of gravitation using the data from the binary pulsar 1913 +16, University of Toronto Report, August 1981; Kisher, T. P. (1985).Physical Review D,32, 329; Will, M. C. (1989).Physical Review Letters,62, 369.
Moffat, J. W. (1985). Experimental consequences of the nonsymmetric gravitation theory including the apsidal motion of binaries, Lecture given at the conference on General Relativity and Relativistic Astrophysics, University of Dalhouse, Halifax, Nova Scotia, April 1985.
Mcdow, J. C. (1983). Testing the nonsymmetric theory of graviation, Ph.D. thesis, University of Toronto; Huffman, J. A., Masshal, H. L., and Lewin, W. G. H. (1978).Nature,271, 630.
Bergman, P. G. (1968).International journal of Theoretical Physics,1, 52.
Trautman, A. (1970).Reports of Mathematical Physics,1, 29.
Utiyama, R. (1956).Physical Review,101, 1597.
Stacey, F. D., Tuck, G. J., Moore, G. J., Holding, S. C., Goldwin, B. D., and Zhou, R. (1987).Review of Modern Physics,59, 157; Ander, M. E., Goldman, T., Hughs, R. J., and Nieto, M. M. (1988).Physical Review Letters,60, 1225; Eckhardt, D. H., Jekeli, C., Lazarewicz, A. R., Romaides, A. J., and Sands, R. W. (1988).Physical Review Letters,60, 2567; Moore, G. I., Stacey, F. D., Tuck, G. J., Goodwin, B. D., Linthorne, N, P., Barton, M. A., Reid, D. M., and Agnew, G. D. (1988).Physical Review D,38, 1023.
Fischbach, E., Sudarsky, D., Szafer, A., Tolmadge, C., and Arnson, S. H. (1985).Physical Review Letters,56, 3.
Thieberg, P. (1987).Physical Review Letters,58, 1066.
Wesson, P. S. (1980).Physics Today,33, 32.
illies, G. T., and Ritter, R. C. (1984). Experiments on variation of the gravitational constant using precision rotations, inPrecision Measurements and Fundamental Constants II, B. N. Taylor and W. D. Phillips, eds., National Bureau of Standards, Special Publication 617, p. 629.
Rayski, J. (1965). Unified theory and modern physics,Acta Physica Polonica,28, 89.
obayashi, S., and Nomizu, K. (1963).Foundation of Differential Geometry, Vols. I and II, New York; Kobayashi, S. (1972).Transformation Groups in Differential Geometry, Springer-Verlag, Berlin.
Lichnerowicz, A. (1955).Théorié globale des connexions et de group d'holonomie, Cremonese, Rome.
Hermann, R. (1978). Yang-Mills, Kaluza-Klein and the Einstein program, Math. Sci. Press, Brookline, Massachusetts; Coquereaux, R., and Jadczyk, A. (1988).Riemannian Geometry, Fibre Bundle, Kaluza-Klein Theory and All That ..., World Scientific, Singapore.
Zalewski, K. (1987).Lecture on Rotational Group, PWN, Warsaw [in Polish]; Barut, A. O., and Raczka, R. (1980).Theory of Group Representations and Applications, PWN, Warsaw.
Moffat, J. W. (1978).Physical Review D,19, 3562.
Kalinowski, M. W. (1986). Comment on the nonsymmetric Kaluza-Klein theory with material sources,Zeitschrift für Phisik C (Particles and Fields),33, 76.
Moffat, J. W. (1979).Physical Review D,19, 3557.
Moffat, J. W. (1981).Physical Review D,23, 2870.
Moffat, J. W., and Woolgar, E. (1984). The apsidal motion of the binary star in the nonsymmetric gravitational theory, University of Toronto Report; Moffat, J. W. (1984). The orbital motion of DI Hercules as a test of the theory of gravitation, University of Toronto Report.
De Groot, S. R., and Suttorp, R. G. (1972).Foundations of Electrodynamics, North-Holland, Amsterdam.
Plebański, J. (1970).Nonlinear Electrodynamics, Nordita, Copenhagen.
Kalinowski, M. W. (1981).Letters in Mathematical Physics,5, 489; Kalinowski, M. W. (1958). Torsion and the Kaluza-Klein theory,Acta Physica Austriaca 27, 45.
Hlavaty, V. (1952).Journal of Rational Mechanics and Analysis 1, 539; Hlavaty, V. (1953).Journal of Rational Mechanics and Analysis,2, 2, 223. Hlavaty, V. (1955).Journal of Rational Mechanics and Analysis,4, 247, 654.
Wyman, M. (1950).Canadian Journal of Mathematics,427.
Lanczos, C. (1970).The Variational Principles of Mechanics, University of Toronto Press, Toronto, Ontario, Canada.
Klotz, A. H. (1983).Macrophysics and Geometry, Cambridge University Press, Cambridge; Klotz, A. H. (1988). Plane waves in the generalized field theory,Acta Physica Polonica B,19, 533.
Kalinowski, M. W. (1982).Physical Review D,26, 3419.
Einstein, A. (1950).Canadian Journal of Mathematics,2, 120.
Duff, M. J., Nilson, B. E. W., and Pope, C. N. (1986).Physics Reports,130, 1.
Arkuszewski, W., Kopczyński, W., and Ponomaviev, V. N. (1974).Annales de l'Institut Henri Poincaré A,21, 89.
Mann, R. B. (1982). Investigations of an alternative theory of gravitation, Ph.D. thesis, University of Toronto, Toronto, Ontario, Canada.
Mann, R. B., and Moffat, J. W. (1981).Journal of Physics A,14, 2367;Journal of Physics A,15, 1055.
Moffat, J. W., and Boal, D. H. (1975).Physical Review D,11, 1375.
Pant, N. D. (1975).Nuovo Cimento,25B, 175.
Papapetrou, A. (1948).Proceedings of the Royal Irish Academy,52, 96.
Bonnor, W. B. (1951).Proceedings of the Royal Society,210, 427.
Bonnor, W. B. (1951).Proceedings of the Royal Society,209, 353.
Vanstone, J. R. (1962).Canadian Journal of Mathematics,14, 568.
Born, M., and Infeld, L. (1934).Proceedings of the Royal Society A,144, 425.
Abraham, M. (1903).Annalen der Physik,10, 105; Cushing, J. T. (1981).American Journal of Physics,49, 1133.
Campbell, L., and Moffat, J. W. (1982). Black holes in the nonsymmetric theory of gravitation, University of Toronto Report, Toronto, Ontario, Canada.
Demiański, M. (1986).Foundations of Physics,16, 187.
Wheeler, J. A. (1955).Physical Review,97, 511.
Wong, S. K. (1970).Nuovo Cimento A,65, 689.
Dicke, R. H. (1962).Review of Modern Physics,34, 116.
Brans, C., and Dicke, R. H. (1961).Physical Review,124, 925.
Nielsen, H. B., and Patkos, A. (1982).Nuclear Physics B,195, 137.
Fujii, Y. (1975).General Relativity and Gravitation,6, 29.
Gibbons, G. W., and Whitting, B. F. (1981).Nature,291, 636.
Glass, E. N., and Szamosi, G. (1987).Physical Review D,35, 1205.
Bars, J., and Vissers, M. (1986).Physical Review Letters,57, 25.
Sherk, J. (1979).Physics Letters,88B, 265.
Barr, S. M., and Mohapatra, R. N. (1987).Physical Review Letters,57, 3129.
Adelberger, E. G., Stubbs, C. W., Rogers, W. F., Raab, F. J., Heckal, B. R., Gundlach, J. M., Swanson, H. E., and Wantable, R. (1987).Physical Review Letters,59, 59.
Kogut, J. B. (1982).Review of Modern Physics,55, 182.
Lee, T. D. (1979).Physical Review D,19, 1802.
Lee, T. D. (1981).Particle Physics and Introduction to Field Theory, Herwood, New York.
Lehman, H., and Wu, Tsai Tsu (1984).Nuclear Physics B,237, 205; Lehman, H., and Wu, Tsai Tsu (1985).Communications in Mathematical Physics,97, 161.
Kramer, D., Stephani, H., MacCallum, M., and Herlt, E. (1980).Exact Solution of Einstein's Field Equations, Cambridge University Press, Cambridge; Lai, K. B., and Ali, N. (1969). Plane wave solutions of Einstein's unified field equations of nonsymmetric theories in Bondi space-time,Tensor N. S.,20, 131 (1969); Lai, K. B., and Ali, N. (1956). The ((t/z)-type plane wave solutions of the field equations of Einstein's non-symmetric unified field theory in Bondi space-time,Tensor N.S.,6, 299; Takeno, H. (1957). Some wave solutions of Einstein's generalized theory of gravitation,Tensor N. S.,6, 69; Takeno, H. (1957). On some generalized plane wave solutions of non-symmetric unified theory,Tensor N. S.,7, 34; Takeno, H. (1958). On some generalized plane wave solutions of non-symmetric unified field theory, II,Tensor N.S.,8, 71; Zakharow, V. D. (1972).Gravitational Waves in Einstein's Theory of Gravitation, Nauka, Moscow [in Russian].
Mann, R. B., and Moffat, J. W. (1982).Physical Review D,25, 4310.
Mann, R. B., and Moffat, J. W. (1982).Physical Review D,26, 1858.
Bryan, R. A., and Scott, B. L. (1964).Physical Review,135, B434; Brown, G. E. (1972). InElementary Particle Models of Two Nucleon Force, S. M. Austin and G. M. Crawley, eds., Plenum Press, New York, p. 29; Mau Vinh, R. (1977). Nucleon-nucleon potentials and theoretical developments. An overview of the nucleon-nucleon interactions, inNucleon-Nucleon Interaction, ATP Conference Proceedings, No. 41, p. 140.
Rho, M. (1984). Pion interactions within nuclei,Annual Review of Nuclear and Particle Science,14, 54.
De Tar, C. E., and Donoghue, J. F. (1983). Bag model of hadrons,Annual Review of Nuclear and Particle Science,33, 235.
Goldflam, R., and Wilets, L. (1982).Physical Review D,25, 1951.
Friedberg, R., and Lee, T. D. (1978). Quantum chromodynamics and the soliton models of hadronsPhysical Review D,18, 2623.
Isham, C. J., Salam, A., and Strathdee, J. (1971).Physical Review D,3, 867.
Tafel, J., and Trautman, A. (1983).Journal of Mathematical Physics,24, 1087.
Kalinowski, M. W. (1986).International Journal of Theoretical Physics,25, 327; Kalinowski, M. W. (1985/1986). Can we get confinement in QCD from higher dimensions,Annales Universitatis Mariae Curie-Sklodowska Sectio AAA,XL/XLI (21), 263.
Peradzyński, Z. (1981). Geometry of nonlinear interactions in partial differential equations, Institute of Fundamental Problems in Technology of Polish Academy of Sciences Report, Warsaw [in Polish]; Grundland, A., and Zelazny, R. (1983).Journal of Mathematical Physics,24, 2305;Journal of Mathematical Physics,24, 2315; Kalinowski, M. W. (1982).Letters in Mathematical Physics,6, 17; Kalinowski, M. W. (1983).Letters in Mathematical Physics,7, 479; Kalinowski, M. W. (1984).Journal of Mathematical Physics,25, 2620; Kalinowski, M. W., and Grundland, A. (1986).Journal of Mathematical Physics,27, 1906; Kalinowski, M. W. (1985).International Journal of Theoretical Physics,24, 957; Bullough, R. K., and Caudrey, P. J., ed. (1980).Solitons, Springer-Verlag, Berlin; Eilenberg, G. (1983).Solitons, Mathematical Methods for Physicists, Springer-Verlag, Berlin; Novikov, P. S., ed. (1980).Theory of Solitons, the Inverse Scattering Method, Mir, Moskow [in Russian]; Chodos, A., Hadjimichael, E., and Tze, C., eds. (1984).Solitons in Nuclear and Elementary Particle Physics, World Scientific Singapore.
Skyrme, R. H. T. (1961).Proceedings of the Royal Society A,260, 127; 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, Miramare-Trieste, p. 170; Kölbermann, G., and Eisenberg, J. M. (1987).Physics Letters B,188, 311; Kölbermann, G., Eisenberg, J. M., and Silbar, R. R. (1986).Physics Letters B,179, 4; Kölbermann, G., and Eisenberg, J. M. (1988). Further investigations of the NN interaction in the Skyrme model, Preprint, Institut für Theoretische Physik, Frankfurt Universität.
Thomas, A. W. (1982). Chiral symmetry and the bag model: A new starting point for nuclear physics, TH3368-CERN TRI-PP-82-29.
Mihich, L. (1983).Nuovo Cimento,70B, 115.
Bekenstein, D. J. (1977).Physical Review D,15, 1458.
Hamel, G. (1949).Theoretische Mechanik, Berlin.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kalinowski, M.W. Nonsymmetric Kaluza-Klein and Jordan-Thiry theory in a general non-Abelian case. Int J Theor Phys 30, 281–399 (1991). https://doi.org/10.1007/BF00674972
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00674972