Communications in Mathematical Physics

, Volume 30, Issue 1, pp 1–10 | Cite as

Necessary and sufficient conditions for current conservation in the framework of Relativistic Quantum Field Theory

  • Eldad Gal-Ezer


Necessary and sufficient conditions for the conservation of vector currents covariant under translations and of the Conformal currents, are formulated and proven. Only the weak spectrum condition is assumed, thus the theorems serve as generalizations of a well-known theorem due to Coleman. This is done under the axioms of Relativistic Quantum Field Theory due to Wightman.


Neural Network Statistical Physic Field Theory Complex System Quantum Field Theory 
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.
    Gal-Ezer, E.: Nuovo Cimento A10, 682 (1972).Google Scholar
  2. 2.
    Streater, R. F., Wightman, A. S.: PCT, Spin & Statistics and All That. New York: Benjamin 1964.Google Scholar
  3. 3.
    The original treatment, in which heuristic arguments are given, is Coleman, S.: J. Math. Phys.7, 787 (1966). A review article, in which a rigorous formulation and proof is outlined and which contains previous references, is Orzalesi, G. A.: Rev. Mod. Phys.42, 381 (1970). For a formulation and proof of a Coleman Theorem for the case of Conformal symmetry, see Bose, S. K., McGlinn, W. D.: Phys. Rev.D4, 342 (1971).Google Scholar
  4. 4.
    Schwartz, L.: Application of distributions to the theory of elementary particles in quantum mechanics. New York: Gordon and Breach, 1968.Google Scholar
  5. 5.
    d μ(x) andK μν(x) are the currents generating the conformal group and θμν(x) is the “improved energy momentum tensor”. See Callan, C. G., Jr., Coleman, S., Jackiw, R.: Ann. Phys. (N.Y.)59, 42 (1970); Gell-Mann, M.: Proceedings of the 3rd Hawaii Topical Conference in Particle Physics, 1969 (Western Periodicals Co., Los Angeles).Google Scholar
  6. 6.
    Källen, G.: Helv. Phys. Acta25, 417 (1952); Lehman, H.: Nuovo Cimento11, 342 (1954).Google Scholar
  7. 7.
    Wightman, A. S., Gårding, L.: Arkiv för Fysik28, 129 (1965); Reeh, H.: Commun. math. Phys.14, 315 (1969).Google Scholar
  8. 8.
    Gårding, L., Lions, J. L.: Functional analysis, Suppl. A1 Vol. XIV. Del Nuovo Cimento (1959).Google Scholar
  9. 9.
    Wightman, A. S.: Relativistic invariance and quantum mechanics. Suppl. A1 Vol. XIV Del Nuovo Cimento (1959).Google Scholar
  10. 10.
    Epstein, H., Hepp, K., Nuyts, J.: Quantum field theory seminar notes. Princeton (1966), unpublished preprint.Google Scholar
  11. 11.
    Reeh, H.: Coleman's Theorem, unpublished seminar talk, Max-Planck-Institut für Physik und Astrophysik.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Eldad Gal-Ezer
    • 1
  1. 1.Dept. of Physics & AstronomyTel-Aviv University, Ramat AvivTel-AvivIsrael

Personalised recommendations