Skip to main content
SpringerLink
Log in

On the quantum conditions in field theory — IV

  • Published:
Il Nuovo Cimento (1955-1965)

Summary

We apply the covariant functional formalism to the Feynman-Gell-Mann spinorial equation. We extend the first order approximation of the W.K.B. method to field theory, giving the corresponding quantum conditions. Applying these results to free fields, we find a relationship between various quantum numbers in field theory. For coupled fields we find indications for a further treatment of the problem.

Riassunto

Si applica il formalismo funzionale covariante all’equazione spinoriale di Feynman-Gell-Mann. Si estende l’approssimazione al primo ordine del metodo W.K.B. alla teoria dei campi dando le corrispondenti condizioni quantiche. Applicando questi risultati ai campi liberi si trovano delle relazioni fra i vari numeri quantici nella teoria dei campi. Per campi accoppiati si hanno indicazioni per una ulteriore trattazione del problema.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. S. Liotta:Nuovo Cimento,3, 438 (1956);8, 798 (1958);13, 921 (1959); referred to respectively as Parts I, II, III; and14, 443 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  2. N. Bohr:Phil. Mag.,26, 1 (1913).

    Article  MATH  Google Scholar 

  3. W. Wilson:Phil. Mag.,28, 795 (1915).

    Article  Google Scholar 

  4. Ishiwara:Tokyo Math. Phys. Proc.,8, 106 (1915).

    Google Scholar 

  5. A. Sommerfeld:Ann. der Phys.,51, 1 (1916).

    Article  ADS  Google Scholar 

  6. R. P. Feynman andM. Gell-Mann:Phys. Rev.,109, 193 (1958).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. J. B. Keller:Ann. Phys.,4, 180 (1958).

    Article  ADS  MATH  Google Scholar 

  8. L. Fantappiè:I funzionali analitici, in Mem. Acc. Naz. Linc. serie vi,3, fasc. xi (1930).

  9. J. Schwinger:Phys. Rev.,74, 1439 (1948).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. E. Persico:Fondamenti della meccanica atomica (1936).

  11. G. Wentzel:Quantum Theory of Fields (1949).

  12. A. Sommerfeld:Atomic Structure and Spectral Lines, English translation (1923), p. 551 on.

  13. J. Hamilton:The Theory of Elementary Particles (1959).

Download references

Author information

Author notes

  1. R. S. Liotta

    Present address: Istituto di Fisica dell’Università, Roma and Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy

Authors and Affiliations

  1. Department of Physics, Columbia University, New York, N. Y.

    R. S. Liotta

Authors
  1. R. S. Liotta
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liotta, R.S. On the quantum conditions in field theory — IV. Nuovo Cim 17, 703–725 (1960). https://doi.org/10.1007/BF02727561

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02727561

Search

Navigation