Geodesic
Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized Feynman amplitudes
Teoretičeskaâ i matematičeskaâ fizika, Tome 59 (1984) no. 3, pp. 373-387 Cet article a éte moissonné depuis la source Math-Net.Ru

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An absolutely convergent $\alpha$ representation of analytically and (or) dimensionally regularized Feynman.amplitudes is obtained on different sections of the domain of analyticity with respect to the regularizing parameters. The representation differs from the $\alpha$ representation in the original domain of absolute convergence by the presence in the integrand of an operator $\mathscr R^*$, which has the same structure as the $R^*$ operation that generalizes dimensional renormalization when not only ultraviolet but also infrared poles are present. The operator $\mathscr R^*$ explicitly realizes analytic continuation of the parametric integral and can be expressed in terms of the ultraviolet subtracting operators and also in terms of the infrared subtracting operators that generate a Maclaurin expansion in the coordinate space. 
@article{TMF_1984_59_3_a4,
     author = {V. A. Smirnov},
     title = {Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized {Feynman} amplitudes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {373--387},
     year = {1984},
     volume = {59},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_59_3_a4/}
}
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V. A. Smirnov. Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized Feynman amplitudes. Teoretičeskaâ i matematičeskaâ fizika, Tome 59 (1984) no. 3, pp. 373-387. http://geodesic.mathdoc.fr/item/TMF_1984_59_3_a4/

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