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By Y. Choquet-Bauhat, et al.,

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Lam, Asymptotic expansion of Feynman amplitudes. Part 1: the convergent case. Commun. Math. Phys. 39, 1 (1974) 39. N. Usyukina, On a representation for three point function. Teor. Mat. Fiz. 22, 300–306 (1975) 40. A. Kotikov, Differential equations method: new technique for massive Feynman diagrams calculation. Phys. Lett. B 254, 158–164 (1991) 41. A. Kotikov, Differential equations method: the calculation of vertex type Feynman diagrams. Phys. Lett. B 259, 314–322 (1991) 42. A. Kotikov, Differential equation method: the calculation of N point Feynman diagrams.

Pn ) f =1 ≡ lim t0 →∞(1−i ) 0 p1 p2 . . A. where | p A p B 0 and | p1 p2 . . pn 0 denote the wave functions of the initial- and final-state free particles, HI is the Hamiltonian in the interaction picture, and T is the operator of time-ordering. ” means only the connected and amputated Feynman diagrams need to be considered. The right-hand side of the above equation is hard to calculate analytically, and usually expanded in series, © Springer-Verlag Berlin Heidelberg 2016 J. 4) Each contribution from the series can be illustrated by a kind of Feynman diagrams.

Rev. Lett. 30, 1343–1346 (1973) D. Gross, F. Wilczek, Asymptotically free gauge theories. 1. Phys. Rev. D 8, 3633–3652 (1973) G. ’t Hooft, Renormalization of massless yang-mills fields. Nucl. Phys. B 33, 173–199 (1971) H. Yukawa, Quantum theory of nonlocal fields. 1. Free fields. Phys. Rev. 77, 219–226 (1950) H. Yukawa, Quantum theory of nonlocal fields. 2: irreducible fields and their interaction. Phys. Rev. 80, 1047–1052 (1950) A. Pais, G. Uhlenbeck, On field theories with nonlocalized action.

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Analysis, Manifolds and Physics [Part 2] by Y. Choquet-Bauhat, et al.,

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