The Disordered Universe 2025: Analytic Properties of Amplitudes and Correlators
Abstract
These lectures provide an introduction to modern techniques for studying the analytic properties of loop-level scattering amplitudes and correlation functions in perturbative quantum field theory. We begin by developing the ideas behind Landau analysis, which identifies the location and nature of kinematic singularities in Feynman integrals (the universal building blocks that contribute to perturbative amplitudes and correlators). We then show how fundamental principles such as unitarity and causality constrain the analytic structure of Feynman integrals, and develop methods for working out some of these constraints in practice. Finally, we connect these observations to the properties of iterated integrals and their symbol calculus, to show how bootstrap methods can be used to determine the functional form of Feynman integrals from just knowledge of their analytic structure. These notes are based on a series of lectures held during the La Ricotta Summer School "The Disordered Universe 2025" from 21~July to 1~August~2025.
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BibTeX
@misc{capuano2026disordered,
title = {{The Disordered Universe 2025: Analytic Properties of Amplitudes and Correlators}},
author = {Mattia Capuano and Chandramouli Chowdhury and Chantelle Esper and Alessandro Palazio and Jonah Stalknecht and Yong Sheng Yap and Andrew J. McLeod and Paolo Benincasa and Guilherme Leite Pimentel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36271},
eprint = {2610.36271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36271},
}
RIS
TY - UNPB
TI - The Disordered Universe 2025: Analytic Properties of Amplitudes and Correlators
AU - Mattia Capuano
AU - Chandramouli Chowdhury
AU - Chantelle Esper
AU - Alessandro Palazio
AU - Jonah Stalknecht
AU - Yong Sheng Yap
AU - Andrew J. McLeod
AU - Paolo Benincasa
AU - Guilherme Leite Pimentel
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36271
UR - https://arxiv.org/abs/2610.36271
AB - These lectures provide an introduction to modern techniques for studying the analytic properties of loop-level scattering amplitudes and correlation functions in perturbative quantum field theory. We begin by developing the ideas behind Landau analysis, which identifies the location and nature of kinematic singularities in Feynman integrals (the universal building blocks that contribute to perturbative amplitudes and correlators). We then show how fundamental principles such as unitarity and causality constrain the analytic structure of Feynman integrals, and develop methods for working out some of these constraints in practice. Finally, we connect these observations to the properties of iterated integrals and their symbol calculus, to show how bootstrap methods can be used to determine the functional form of Feynman integrals from just knowledge of their analytic structure. These notes are based on a series of lectures held during the La Ricotta Summer School "The Disordered Universe 2025" from 21~July to 1~August~2025.
ER -