Unified Theory of Fundamental Interactions

  • Behram Kursunoglu
Part of the Studies in the Natural Sciences book series (SNS, volume 5)


The field equations of the generalized theory of gravitation which were proposed over 20 years ago by this author have now been solved for the static spherically symmetric case. It is found that electric and magnetic charges are two fundamental constants of integration and that the corresponding electric, magnetic and gravitational fields are regular everywhere only if the magnetic charge g ≠ 0. The magnetic charge g assumes an infinite spectrum of values and is a function of mass. For g = 0, the solutions reduce to the Nordström solution of general relativity in the limit of large r. The theory leads to elementary particles of finite self-energy \((\Delta ( \pm E) = m{c^2} - \frac{{{{(2{g_o})}^2}}}{{{\ell _o}}})\) and binding energy. The structure of an elementary particle which is due to the existence of finite ±g consists of a magnetically neutral core of matter containing a distribution of magnetic charge density in stratified layers of sharply decreasing magnitude and alternating signs so that magnetic monopoles associated with a long range field do not exist. As a consequence of the general covariance of the theory the surfaces of zero magnetic charge density in the core of an elementary particle have an indeterminacy. These facts lead to a mass spectrum for the elementary particles. In addition to charged electric and magnetic currents, the theory yields electrically and magnetically neutral currents and the corresponding fields. The neutral current and the corresponding neutral field are the classical counterparts of the vacuum polarization in quantum electrodynamics. For every positive energy solution there exists also a negative energy solution with the corresponding electric and magnetic charges. For g = 0, the volume integral of the neutral electric current density diverges. The assymmetry of Maxwell’s equations with regard to the absence of a magnetic current can be understood because the neutral and charged magnetic currents are localized in the core of elementary particle generating short range fields alone.

Furthermore, the theory yields two lengths of the dimensions of 10−25 cm and 10−15 cm which could serve to differentiate between leptonic and hadronic processes as well as a length 10−34 cm referring to the minimum size to which an elementary particle could have collapsed (micro-black-holes).

The presence of negative energy solutions along with positive energy solutions point to a large scale symmetry with respect to a distribution of matter and antimatter in the universe.


Field Equation Gravitational Field Fundamental Interaction Unify Theory Magnetic Charge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. Kursunoglu, Phys. Rev. 88, 1369 (1952).MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    B. Kursunoglu, Rev. Mod. Phys. 29, 412 (1957).MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    B. Kursunoglu, Nuovo Cimento 15, Series X, 729 (1960).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Einstein and Schrödinger versions of the generalized theory of gravitation, (5,6,7,8) because of the absence of a correspondence principle in them, do not yield equations (II. 57). In fact the Einstein and Schrödinger theories are obtained from the present one by setting r0 = ∞ (!). Hence these theories cannot yield Lorentz’s equations of motion.Google Scholar
  5. 5.
    A. Einstein, Can. J. Math. 2, 120 (1950).MATHCrossRefGoogle Scholar
  6. 6.
    B. Kaufman, Helv. Physica Acta Supp. 4, 227 (1956).Google Scholar
  7. 7.
    A. Einstein and B. Kaufman, Ann. Math. 62, 128 (1955).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    A. Papapetrou, Proc. Roy. Irish Acad. Vol. LII, Sec. A, No. 6, 69 (1948).Google Scholar
  9. 9.
    The presence of a short range neutral charge density J4 0 may be thought of as the classical version of the vacuum polarization in quantum electrodynamics.Google Scholar
  10. 10.
    In this theory the correspondence with general relativity plus Maxwell’s equations is based on setting a physical constant like magnetic charge g equal to zero while in quantum theory correspondence with classical mechanics is obtained by setting h=0. However, if a relation between the g of this theory and h can. be established then in this theory also the correspondence principle can be satisfied by setting h = 0 everywhere.Google Scholar
  11. 11.
    The nonconservation of the neutral charge density for g = 0 can be compared to the divergence of the vacuum polarization in quantum electrodynamics.Google Scholar
  12. 12.
    P.A.M. Dirac, Phys. Rev. 74, 817 (1948).MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    J. Schwinger, Proceedings of Coral Gables Conference, Symmetry Principles at High Energy, (Freeman, San Francisco, 1966) Eds. A. Perlmutter, et al.Google Scholar
  14. 14.
    E. Schrödinger, Proc. Roy. Irish Acad. LI, A213 (1948).Google Scholar
  15. 15.
    The functions Φ and Г are expressible in terms of Ω and Λ and are therefore invariant under coordinate transformations.Google Scholar
  16. 16.
    Because of (III.18), (IV.3) and also in view of the spectrum of values assumed by the magnetic charge, the radius R remains invariant under coordinate transformations.Google Scholar
  17. 17.
    We observe that because of the invariance of the function Φ (r) and the relation t=tan Φ all the statements concerning the core of an elementary particle are in complete agreement with the principle of general covariance.Google Scholar

Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • Behram Kursunoglu
    • 1
  1. 1.Center for Theoretical StudiesUniversity of MiamiCoral GablesUSA

Personalised recommendations