A brief Introduction to Dispersion Relations and Analyticity

Abstract

In these lectures we provide a basic introduction into the topic of dispersion relation and analyticity. The properties of 2-point functions are discussed in some detail from the viewpoint of the Källén-Lehmann and general dispersion relations. The Weinberg sum rules figure as an application. The analytic structure of higher point functions in perturbation theory are analysed through the Landau equations and the Cutkosky rules.

arXiv comment28 pages, 11 figures, Lectures given at Dubna School: "Strong Fields and Heavy Quarks", July 2016

References in corpus (6)

• On Renormalization Group Flows in Four Dimensions
• Lectures on differential equations for Feynman integrals
• Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral
• Exclusive Chromomagnetism in heavy-to-light FCNCs
• Cutkosky Rules and Outer Space
• The rigorous analyticity-unitarity program and its successes

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• Ultraviolet-complete quantum field theories with fractional operators
• Long-range Ising interactions mediated by $\lambda {\varphi }^4$ fields: probing the renormalisation of sound in crystals of trapped ions