This book provides a comprehensive, pedagogical introduction to scattering amplitudes in gauge theory and gravity for graduate students.

The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.

Providing a comprehensive, pedagogical introduction to scattering amplitudes in gauge theory and gravity, this book is ideal for graduate students and researchers. It offers a smooth transition from basic knowledge of quantum field theory to the frontier of modern research. Building on basic quantum field theory, the book starts with an introduction to the spinor helicity formalism in the context of Feynman rules for tree-level amplitudes. The material covered includes on-shell recursion relations, superamplitudes, symmetries of N=4 super Yang–Mills theory, twistors and momentum twistors, Grassmannians, and polytopes. The presentation also covers amplitudes in perturbative supergravity, 3D Chern–Simons matter theories, and color-kinematics duality and its connection to 'gravity=(gauge theory)x(gauge theory)'. Basic knowledge of Feynman rules in scalar field theory and quantum electrodynamics is assumed, but all other tools are introduced as needed. Worked examples demonstrate the techniques discussed, and over 150 exercises help readers absorb and master the material.

A short, graduate-level synthesis of recent developments in theoretical physics, from a pioneer in the field Lectures 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 included Concise and accessible pedagogical approach Topics include soft theorems, the memory effect, asymptotic symmetries with applications to QED, Yang-Mills theory, quantum gravity, and black holes

Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the broader fields of mathematical physics.

This volume provides a self-contained introduction to applications of loop representations in particle physics and quantum gravity, in order to explore the gauge invariant quantization of Yang-Mills theories and gravity. First published in 1996, this title has been reissued as an Open Access publication on Cambridge Core.

Feynman’s bestselling introduction to the mind-blowing physics of QED—presented with humor, not mathematics Celebrated for his brilliantly quirky insights into the physical world, Nobel laureate Richard Feynman also possessed an extraordinary talent for explaining difficult concepts to the public. In this extraordinary book, Feynman provides a lively and accessible introduction to QED, or quantum electrodynamics, an area of quantum field theory that describes the interactions of light with charged particles. Using everyday language, spatial concepts, visualizations, and his renowned Feynman diagrams instead of advanced mathematics, Feynman clearly and humorously communicates the substance and spirit of QED to the nonscientist. With an incisive introduction by A. Zee that places Feynman’s contribution to QED in historical context and highlights Feynman’s uniquely appealing and illuminating style, this Princeton Science Library edition of QED makes Feynman’s legendary talks on quantum electrodynamics available to a new generation of readers.

This thesis proposes a new perspective on scattering amplitudes in quantum field theories. Their standard formulation in terms of sums over Feynman diagrams is replaced by a computation of geometric invariants, called intersection numbers, on moduli spaces of Riemann surfaces. It therefore gives a physical interpretation of intersection numbers, which have been extensively studied in the mathematics literature in the context of generalized hypergeometric functions. This book explores physical consequences of this formulation, such as recursion relations, connections to geometry and string theory, as well as a phenomenon called moduli space localization. After reviewing necessary mathematical background, including topology of moduli spaces of Riemann spheres with punctures and its fundamental group, the definition and properties of intersection numbers are presented. A comprehensive list of applications and relations to other objects is given, including those to scattering amplitudes in open- and closed-string theories. The highlights of the thesis are the results regarding localization properties of intersection numbers in two opposite limits: in the low- and the high-energy expansion. In order to facilitate efficient computations of intersection numbers the author introduces recursion relations that exploit fibration properties of the moduli space. These are formulated in terms of so-called braid matrices that encode the information of how points braid around each other on the corresponding Riemann surface. Numerous application of this approach are presented for computation of scattering amplitudes in various gauge and gravity theories. This book comes with an extensive appendix that gives a pedagogical introduction to the topic of homologies with coefficients in a local system.

A fully updated edition of the classic text by acclaimed physicist A. Zee Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. The most accessible and comprehensive introductory textbook available Features a fully revised, updated, and expanded text Covers the latest exciting advances in the field Includes new exercises Offers a one-of-a-kind resource for students and researchers Leading universities that have adopted this book include: Arizona State University Boston University Brandeis University Brown University California Institute of Technology Carnegie Mellon College of William & Mary Cornell Harvard University Massachusetts Institute of Technology Northwestern University Ohio State University Princeton University Purdue University - Main Campus Rensselaer Polytechnic Institute Rutgers University - New Brunswick Stanford University University of California - Berkeley University of Central Florida University of Chicago University of Michigan University of Montreal University of Notre Dame Vanderbilt University Virginia Tech University

This volume is a compilation of lectures delivered at the TASI 2016 summer school, 'Anticipating the Next Discoveries in Particle Physics', held at the University of Colorado at Boulder in June 2016. The school focused on topics in theoretical particle physics, phenomenology, dark matter, and cosmology of interest to contemporary researchers in these fields. The lectures are accessible to graduate students in the initial stages of their research careers.