Abstract
The problem of obtaining asymptotic expansions of Feynman integrals in various limits of momenta and masses is a typical mathematical problem in elementary-particle physics. In this book, it is explained how this problem is solved. To characterize, briefly, the main steps of the solution let us consider, for example, the process of e + e − annihilation, where an incoming electron and positron produce, according to the quantum-theoretical description, a virtual photon, e + e − → γ*, which in turn produces some particles, for example a quark—antiquark pair, γ* → \( q\overline q \), which may then be transformed into mesons. The process of quark production is described, in perturbative quantum field theory, by Feynman integrals corresponding to various graphs generated by the Feynman rules. One of the three external legs of such a diagram corresponds to a triple vertex associated with the quark vector current, and the other two external legs correspond to the external quarks. If we are interested in the total cross-section for the production of the quarks the problem reduces to the evaluation of the imaginary part of diagrams contributing to the vacuum polarization and containing only two external vertices for the two vector currents.
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© 2002 Springer-Verlag Berlin Heidelberg
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(2002). Introduction. In: Applied Asymptotic Expansions in Momenta and Masses. Springer Tracts in Modern Physics, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44574-9_1
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DOI: https://doi.org/10.1007/3-540-44574-9_1
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