Mellin-Barnes integrals : a primer on particle physics applications

Mellin-Barnes integrals a primer on particle physics applications

Introduction -- Complex Analysis -- Mellin-Barnes Representations for Feynman and Related Integrals -- Resolution of Singularities -- Analytic Solutions -- Approximations -- Numerical Methods.

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Bibliographische Detailangaben
1. Verfasser: Dubovyk, Ievgen (VerfasserIn)
Weitere Verfasser: Gluza, Janusz (VerfasserIn), Somogyi, Gábor (VerfasserIn)
Format: UnknownFormat
Sprache:eng
Veröffentlicht: Cham Springer 2022
Schriftenreihe:Lecture notes in physics volume 1008
Schlagworte:
Elementary particles (Physics). > Quantum field theory. > Mathematical physics. > Functions of complex variables. > Mathematics. > Elementarteilchenphysik > Störungstheorie > Pfadintegral > Barnes-Integral > Hypergeometrische Reihe > Auflösung von Singularitäten > Numerische Integration
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Beschreibung
Zusammenfassung:Introduction -- Complex Analysis -- Mellin-Barnes Representations for Feynman and Related Integrals -- Resolution of Singularities -- Analytic Solutions -- Approximations -- Numerical Methods.
In this book, the authors discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to achieve the theoretical precision required by experimental setups. In this regard, performing higher-order calculations in perturbative quantum field theory is of paramount importance. The Mellin-Barnes integrals technique has been successfully applied to the analytic and numerical analysis of integrals connected with virtual and real higher-order perturbative corrections to particle scattering. Easy-to-follow examples with the supplemental online material introduce the reader to the construction and the analytic, approximate, and numeric solution of Mellin-Barnes integrals in Euclidean and Minkowskian kinematic regimes. It also includes an overview of the state-of-the-art software packages for manipulating and evaluating Mellin-Barnes integrals. The book is meant for advanced students and young researchers to master the theoretical background needed to perform perturbative quantum field theory calculations.
Beschreibung:xviii, 283 Seiten
Diagramme, Porträts
ISBN:9783031142710
978-3-031-14271-0