, Volume 10, Issue 5, pp 537–544 | Cite as

Partially conserved axial-vector current inS-matrix theory

  • J Pasupathy
  • C A Singh
Nuclear And Particle Physics


Mandelstam’s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm π andm ϱ as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionmϱ2mπ2=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.


Partially conserved axial-vector current Lorentz quantum number dual pion model Adler zeros 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arbab F and Jackson J D 1968Phys. Rev. 176 1796CrossRefADSGoogle Scholar
  2. Brower R C 1971Phys. Lett. B34 143ADSGoogle Scholar
  3. Capella A 1970Nucl. Phys. B22 225CrossRefADSGoogle Scholar
  4. Fubini S and Veneziano G 1971Ann. Phys. 63 12CrossRefADSGoogle Scholar
  5. Halpern M B and Thorn C B 1971Phys. Lett. B35 441ADSGoogle Scholar
  6. Lovelace C 1968Phys. Lett. B28 264ADSGoogle Scholar
  7. Mandelstam S 1968Phys. Rev. 168 1884CrossRefADSGoogle Scholar
  8. Mueller A H 1969Phys. Rev. 172 1516CrossRefADSGoogle Scholar
  9. Neveu A and Schwarz J H 1971Nucl. Phys. B31 86CrossRefADSGoogle Scholar
  10. Neveu A and Thorn C B 1971Phys. Rev. Lett. 27 1758CrossRefADSGoogle Scholar
  11. Neveu A, Schwarz J H and Thorn C B 1971Phys. Lett. B35 529ADSGoogle Scholar
  12. Sawyer R F 1968Phys. Rev. Lett. 21 764CrossRefADSGoogle Scholar
  13. Schwarz J H 1972Phys. Rev. D5 886ADSGoogle Scholar
  14. Schwarz J H and Wallace D J 1972Phys. Rev. D6 723ADSGoogle Scholar
  15. Schwarz J H 1973Phys. Rep. C8 270ADSGoogle Scholar
  16. Sciarrino A and Toller M 1967J. Math. Phys. 8 1252zbMATHCrossRefADSMathSciNetGoogle Scholar
  17. Shapiro J 1969Phys. Rev. 179 1345CrossRefADSGoogle Scholar
  18. Toller M 1965 Univ. of Rome Rep. No. 76Google Scholar
  19. Toller M 1968Nuovo Cimento A53 671Google Scholar
  20. Wang J M and Wang L L 1970Phys. Rev. D1 663ADSGoogle Scholar

Copyright information

© Indian Academy of Sciences 1978

Authors and Affiliations

  • J Pasupathy
    • 1
  • C A Singh
    • 1
  1. 1.Centre for Theoretical StudiesIndian Institute of ScienceBangalore

Personalised recommendations