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vertex function in nonrenormalizable field theory

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Il Nuovo Cimento (1955-1965)

Summary

Au approximate equation is considered for the vertex function Γμ in the nonrenormalizable field theory of interaction between the scalar particles and the massive vector ones. The possibility of formulating some renormalization procedure for the removal of divergences is shown. An iteration method for solving the equation for Γμ is developed. It consists in a successive solution of some simple integral equations. The solutions of these equations are studied and the existence of the unique solution for the renormalized vertex function is proved. This solution is free from divergences, decreases at infinity in the complexp 2-plane and has the logarithmic branch point atg 2=0.

Riassunto

Si studia un’equazione approssimata della funzione di vertice Γμ nella teoria del campo non rinormalizzabile della interazione fra le particelle scalari e quelle vettoriali dotate di massa. Si mostra la possibilità di formulare un procedimento di rinormaizzazione per eliminare le divergenze. Si sviluppa un metodo di iterazione per risolvere l’equazione per Γμ. Esso consiste nella soluzione successiva di alcune semplici equazioni integrali. Si studiano le soluzioni di queste equazioni e si dà la prova dell’esistenza della soluzione unica della funzione di vertice rinormalizzata. Questa soluzione è priva di divergenze, decresce all’inflnito nel pianop 2complesso ed ha un punto di suddivisione logaritmico ag 2=0.

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References

  1. N. N. Bogoltjbov andD. V. Shirkov:Introduction to the Theory of Quantized Fields (Moscow, 1957).

  2. L. B. Okun:Weak Interactions of Elementary Particles (Moscow, 1963).

  3. C. N. Yang andR. L. Mills:Phys. Rev.,96, 191 (1954);J. J. Sakurai:Ann. Phys.,11, 1 (1960).

    Article  MathSciNet  ADS  Google Scholar 

  4. T. D. Lee:Phys. Rev.,128, 899 (1962);Phys. Rev. Lett.,12, 569 (1964).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. T. D. Lee andC. N. Yang:Phys. Rev.,128, 885 (1962).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. V. S. Vanyashin:Zum. Ėksp. Teor. Fiz.,43, 689 (1962).

    MathSciNet  Google Scholar 

  7. G. Feinberg andA. Pais:Phys. Rev.,131, 2724 (1963);133, B 477 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  8. N. N. Khuri andA. Pais:Rev. Mod. Phys.,36, 590 (1964);A. Pais andT. T. Wu:Phys. Rev.,134, B 1303 (1964).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. A. T. Filippov: preprint JINR, (Dubna, 1963), P-1493.

  10. B. A. Arbuzov andA. T. Filippov:Phys. Lett,13, 95 (1964).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. S. Edwards:Phys. Rev.,90, 284 (1953).

    Article  ADS  MATH  Google Scholar 

  12. M. Gell-Mann:Phys. Rev.,125, 1067 (1962).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. G. C. Wick:Phys. Rev.,96, 1124 (1954).

    Article  MathSciNet  ADS  Google Scholar 

  14. E. L. Ince:Ordinary Differential Equations (Kharkov, 1939).

  15. A. Erdelyi (Ed.) :Higher Transcendental Functions, vol.1 (London, 1953).

  16. A. Erdelyi (Ed.):Tables of Integral Transforms, vol.2 (London, 1954).

  17. A. Salam:Phys. Rev.,130, 1287 (1963);A. Salam andR. Deibourgo:Phys. Rev.,135, B 1398 (1964).

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Laboratory of Theoretical Physics, Dubna

    B. A. Arbuzov & A. T. Filippov

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  1. B. A. Arbuzov
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  2. A. T. Filippov
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Arbuzov, B.A., Filippov, A.T. vertex function in nonrenormalizable field theory. Nuovo Cim 38, 796–806 (1965). https://doi.org/10.1007/BF02748598

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