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Titlebook: Evaluating Feynman Integrals; Vladimir A. Smirnov Book 2005 Springer-Verlag Berlin Heidelberg 2005 Alpha and Feynman parameters.Dimensiona

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Feynman Integrals: Basic Definitions and Tools,asic tools such as alpha parameters are presented. Various kinds of regularizations, in particular dimensional one, are presented and properties of dimensionally regularized Feynman integrals are formulated and discussed.
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IBP and Reduction to Master Integrals, down various equations (2.38) for integrals of derivatives with respect to loop momenta and use this set of relations between Feynman integrals in order to solve the reduction problem, i.e. to find out how a general Feynman integral of the given class can be expressed linearly in terms of some mast
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Tables,n’ dependence, −.., of the denominators, which is more natural when the powers of propagators are general complex numbers. As usual, −.. is understood in the sense of −.. − i0, etc. Moreover, denominators with a linear dependence on . are also understood in this sense, e.g. 2. 2. ⋅.−i0, although som
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Analysis of Convergence and Sector Decompositions,m the region of small values of the α-parameters in (2.36), while the off-shell IR divergences arise from the integration over large –.. To reveal these divergences, the integration region is divided into so-called ‘sectors’, where new integration variables are introduced, with the goal to obtain a
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