Titlebook: What is the iε for the S-matrix?; Holmfridur Sigridar Hannesdottir,Sebastian Mizera Book 2022 The Author(s), under exclusive license to Sp

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https://doi.org/10.1007/978-3-031-18258-7Scattering Matrix; Feynman integrals; QFT and Causality; Anomalous thresholds; Landau equation; Schwinger

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集合

Conclusion,This chapter concludes the book with a summary of the results and a list of open questions.

混合

Holmfridur Sigridar Hannesdottir,Sebastian MizeraProvides a pedagogical introduction to the analytic properties of the S-matrix.Reviews the rich literature on singularities of scattering amplitudes.Presents a new prescription for analytically contin

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Unitarity Implies Anomalous Thresholds, the analytic structure of the cuts. We discuss the implications of the cutting rules when unstable particles are involved in the scattering process: we derive how to cut through dressed propagators, and show that cuts through undressed propagators for unstable particles resum to zero.

悠然

Primer on the Analytic S-matrix,elop intuition and illustrate the key points relevant for general multi-loop diagrams. Throughout this chapter, we point out which facets of the analysis generalize straightforwardly and which are more intricate.

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Intrepid

Branch Cut Deformations,cuts can be deformed away to restore the connection between the upper- and lower-half planes, and one when they cannot. Finally, we explain how summing over different Feynman diagrams might result in incompatible . prescriptions and one is forced to consider branch cut deformations to define the complexified amplitude in the first place.

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,Glimpse at Generalized Dispersion Relations, any . scattering process. We find two types of identities: the first relates the scattering amplitude to an integral over its discontinuity, while the second relates parts of the scattering amplitude to an integral over its imaginary part.

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