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Field-theory two-point functions via negative dimension integration

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Abstract

One-loop two-point functions play an important role in quantum field theories, being one of the primary divergent Feynman graphs that calls for regularization and renormalization procedures. These well-known functions are here revisited as illustrative for the power and the simplicity of the negative dimensional integration method (NDIM) approach to tackle Feynman integrals with off-shell external fields and massless and massive virtual fields.

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References

  1. C. G. Bollini and J. J. Giambiagi, Nuovo Ciment. B 12, 20 (1972); C. G. Bollini and J. J. Giambiagi, Phys. Lett. B 40, 566 (1972); G.’ t Hooft and M. Veltman, Nucl. Phys. B 44, 189 (1972); J. F. Ashmore, Lett. Nuovo Cimento 4, 289 (1972).

    Google Scholar 

  2. I. G. Halliday and R. M. Ricotta, Phys. Lett. B 193, 241 (1987); R. M. Ricotta, Topics in Field Theory, PhD Thesis, Imperial College, London, 1987; G. V. Dunne and I. G. Halliday, Phys. Lett. B 193, 247 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  3. A. T. Suzuki and A. G. M. Schmidt, JHEP 9709, 002 (1997); A. T. Suzuki and A. G. M. Schmidt, Eur. J. Phys. C 5, 175 (1998); A. T. Suzuki and A. G. M. Schmidt, Phys. Rev. D 58, 047701 (1998); A. T. Suzuki and A. G. M. Schmidt, J. Phys. A 31, 8023 (1998); A. T. Suzuki, A. G. M. Schmidt and R. Bentin, Nucl. Phys. B 537, 549 (1999); A. T. Suzuki and A. G. M. Schmidt, Eur. Phys. J. C 10, 357 (1999); A. T. Suzuki and A. G. M. Schmidt, Can. J. Phys. 78, 769 (2000); A. T. Suzuki and A. G. M. Schmidt, J. Phys. A 33, 3713 (2000); A. T. Suzuki and A. G. M. Schmidt, J. Comput. Phys. 168, 207 (2001); A. T. Suzuki and A. G. M. Schmidt, Eur. Phys. J. C 19, 391 (2001); A. T. Suzuki and A. G. M. Schmidt, J. Phys. A 35, 151 (2002); A. T. Suzuki, E. S. Santos and A. G. M. Schmidt, Eur. Phys. J. C 26, 125 (2002); A. T. Suzuki, E. S. Santos and A. G. M. Schmidt, J. Phys. A 36, 4465 (2003); A. T. Suzuki, E. S. Santos and A. G. M. Schmidt, J. Phys. A 36, 11859 (2003).

    Article  MathSciNet  ADS  Google Scholar 

  4. I. González and I. Schmidt, Nucl. Phys. B 769, 124 (2007).

    Article  ADS  MATH  Google Scholar 

  5. Y. L. Luke, Mathematical Functions and their Approximations (Academic Press, New York, 1975).

    MATH  Google Scholar 

  6. L. J. Slater, Generalized Hypergeometric Functions (Cambridge University Press, London, 1966).

    MATH  Google Scholar 

  7. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed. (Academic Press, Burlington, MA, 2007).

    MATH  Google Scholar 

  8. A. T. Suzuki, Analytic result for the one-loop massless triangle Feynman diagram, arXiv:0706.1082 hep-th (2007).

  9. P. Appell, Sur les Fonctions Hypergéometriques de Plusieures Variables (Gauthier-Villars, Paris, 1926).

    Google Scholar 

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Correspondence to Alfredo Takashi Suzuki.

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Present address: On leave of absence from May 2011 through April 2012

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Suzuki, A.T. Field-theory two-point functions via negative dimension integration. Journal of the Korean Physical Society 60, 704–713 (2012). https://doi.org/10.3938/jkps.60.704

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  • DOI: https://doi.org/10.3938/jkps.60.704

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