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Differential equations for definition and evaluation of Feynman integrals
Phys. Rev. D 50, 6589 – Published 15 November, 1994
DOI: https://doi.org/10.1103/PhysRevD.50.6589
Abstract
It is shown that every Feynman integral can be interpreted as a Green function of some linear differential operator with constant coefficients. This definition is equivalent to the usual one but needs no regularization and application of the R operation. It is argued that the presented formalism is convenient for practical calculations of Feynman integrals.
References (14)
- N.N. Bogolubov and D.V. Shirkov, Introduction to the Quantum Field Theory (Wiley, New York, 1980).
- J.C. Collins, Renormalization (Cambridge University Press, Cambridge, England, 1984).
- V.A. Smirnov, Renormalization and Asymptotic Expansions (Springer, Berlin, 1991).
- G.'t Hooft and M. Veltman, Nucl. Phys. B44, 189 (1972); C.G. Bollini and J.J. Giambiagi, Nuovo Cimento B 12, 20 (1972); J.F. Ashmore, Lett. Nuovo Cimento 4, 289 (1972); G.M. Cicuta and R. Montaldi, ibid. 4, 329 (1972).
- D.Z. Freedman, K. Johnson and J.I. Lattore, Nucl. Phys. B371, 353 (1992); P.E. Haagensen and J.I. Lattore, Phys. Lett. B 283, 293 (1992); V.A. Smirnov and O.I. Zavialov, Theor. Math. Phys. (Rus.) 96, 288 (1993); Report No. MPI Ph/93 95 (unpublished); V.A. Smirnov, Report No. MPI PhT/94 4 (unpublished).
- P.M. Stevenson, Phys. Rev. D 23, 2916 (1981); G. Grunberg, ibid. 29, 2315 (1984); A. Dhar and V. Gupta, ibid. 29, 2822 (1984); V. Gupta, D.V. Shirkov and O.V. Tarasov, Int. J. Mod. Phys. A 6, 3381 (1991); D.V. Shirkov, Theor. Math. Phys. (Rus.) 93, 466 (1992).
- J.C. Collins, Nucl. Phys. B80, 341 (1974); S. Weinberg, Phys. Rev. D 8, 3497 (1973).
- S. Weinberg, Phys. Rev. 118, 838 (1960).
- E.E. Boos and A.I. Davydychev, Theor. Math. Phys. (Rus.) 89, 56 (1991).
- E. Mendels, Nuovo Cimento A 45, 87 (1978).
- F.A. Berends, M. Buza, M. Böhm, and R. Scharf, Report No. INLO PUB 17 93 (unpublished).
- F.A. Berends and J.B. Tausk, Nucl. Phys. B421, 456 (1994).
- D.J. Broadhurst, Z. Phys. C 47, 115 (1990).
- D.J. Broadhurst, J. Fleisher and O.V. Tarasov, Z. Phys. C 60, 287 (1993).