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Cover; Title; Copyright; Dedication; Contents; Preface; 1. Introduction; 1.1 The Infrared Triangle; 1.2 New Developments; 1.3 Echoing Triangles; 1.3.1 QED, Yang-Mills Theory, Gravity, Massless Particles, . . .; 1.3.2 Leading, Subleading, Sub-Subleading, . . .; 1.3.3 Double Soft Theorems, . . .; 1.3.4 Classical, quantum, . . .; 1.3.5 Minkowski, D 4, Cosmology, . . .; 1.3.6 Supersymmetry, N = 1, 2, . . .; 1.4 Motivation and Applications; 1.4.1 Connecting Disparate Subjects; 1.4.2 Flat Space Holography; 1.4.3 The Gauge Theory S-Matrix; 1.4.4 Miracles in N = 4 Yang-Mills.

1.4.5 Black Holes2. QED; 2.1 Li�A�nard-Wiechert Solution; 2.2 Minkowski Space Penrose Diagram; 2.3 Antipodal Matching Condition; 2.4 Asymptotic Expansions; 2.5 An Infinity of Conserved Charges; 2.6 Canonical Electrodynamics at I; 2.6.1 Symplectic Form; 2.6.2 Commutators; 2.7 Large Gauge Symmetry; 2.8 Ward Identity; 2.8.1 Symmetries of the S-Matrix; 2.8.2 Mode Expansions; 2.8.3 Soft Theorems; 2.9 Feynman Diagrammatics; 2.9.1 Soft Photons; 2.9.2 Soft Gravitons; 2.10 Asymptotic Symmetries; 2.11 Spontaneous Symmetry Breaking, Vacuum Degeneracy, and Goldstone Bosons; 2.12 Massive QED.

2.12.1 Hyperbolic Slices2.12.2 Soft Theorem; 2.13 Magnetic Charges; 2.14 Supersymmetry; 2.14.1 Soft Photino Theorem; 2.14.2 Fermionic Conservation Laws; 2.14.3 N = 4, 8; 2.15 Infrared Divergences; 3. The S-Matrix as a Celestial Correlator; 4. Nonabelian Gauge Theory; 4.1 G-Kac-Moody Algebra; 4.2 Conserved Charges; 5. Gravity; 5.1 Asymptotically Flat Spacetimes; 5.2 Supertranslations; 5.2.1 BMS Analysis; 5.2.2 The Scattering Problem; 5.2.3 Conserved Charges; 5.3 Superrotations; 5.3.1 Conserved Charges; 5.3.2 Symmetries; 5.3.3 Canonical Formalism; 5.3.4 Subleading Soft Theorem.

6. The Memory Effect7. Black Holes; 7.1 The Information Paradox; 7.2 Soft Hair; 7.2.1 Classical Hair; 7.2.2 Horizon Charges; 7.2.3 Quantum Hair; 7.2.4 Electric Hair; 7.3 Discussion; Exercises with Prahar Mitra and Monica Pate; Solutions with Prahar Mitra and Monica Pate; References; Index.

A short, graduate-level synthesis of recent developments in theoretical physics, from a pioneer in the fieldLectures on the Infrared Structure of Gravity and Gauge Theory presents an accessible, graduate-level synthesis of a frontier research area in theoretical physics. Based on a popular Harvard University course taught by the author, this book gives a concise introduction to recent discoveries concerning the structure of gravity and gauge theory at very long distances. These discoveries unite three disparate but well-developed subjects in physics. The first subject is the soft theorems, which were found by particle physicists in the 1950s to control the behavior of low-energy photons and are essential for all collider predictions. The second subject is asymptotic symmetries, found by general relativists in the 1960s to provide a surprising, infinite number of exact relations between distinct physical phenomena. The third subject is the memory effect, the measurement of which is sought in upcoming gravitational wave observations. An exploration of the physical and mathematical equivalence of these three subjects has provided a powerful new perspective on old results and led to a plethora of new results, involving symmetries of QED, gluon scattering amplitudes, flat-space holography in quantum gravity, black hole information, and beyond. Uniquely connective and cutting-edge, Lectures on the Infrared Structure of Gravity and Gauge Theory takes students and scholars to the forefront of new developments in the discipline. Materials are presented in a "lecture notes" style with problem sets includedConcise and accessible pedagogical approachTopics include soft theorems, the memory effect, asymptotic symmetries with applications to QED, Yang-Mills theory, quantum gravity, and black holes.

Includes bibliographical references (pages 169-180) and index.

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