By Vladimir A. Smirnov
Introduction.- Feynman Integrals: easy Definitions and Tools.-Evaluating through Alpha and Feynman Parameters.- zone Decompositions.- comparing by way of Mellin-Barnes Representation.- Integration through elements and aid to grasp Integrals.- evaluate by way of Differential Equations.- comparing grasp Integrals by way of Dimensional Recurrence and Analyticity.- Asymptotic Expansions in Momenta and Masses.- Tables.- a few exact features- Summation Formulae.- desk of MB Integrals.- a short assessment of a few different equipment
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Extra resources for Analytic tools for Feynman integrals
In fact, such integrals will be mainly considered in this book as examples illustrating the methods described. However, in every concrete example considered below, we will see that every Feynman diagram is indeed an analytical function of d, both in intermediate steps of a calculation and, of course, in our results. 5 Besides , the problem of defining UV and IR divergent Feynman integrals within dimensional regularization was studied in  where Mellin–Barnes integrals were applied for this purpose.
An obvious way of regularizing Feynman integrals is to introduce a cut-off at large values of the loop momenta. Another well-known regularization procedure is the Pauli–Villars regularization , which is described by the replacement p2 1 1 1 → 2 − 2 2 2 −m p −m p − M2 22 2 Feynman Integrals: Basic Definitions and Tools and its generalizations. For finite values of the regularization parameter M, this procedure clearly improves the UV asymptotics of the integrand. Here the limiting value of the regularization parameter is M = ∞.
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Analytic tools for Feynman integrals by Vladimir A. Smirnov