Quantum Field Theory and Manifold Invariants

This volume contains lectures from the Graduate Summer School Quantum Field Theory and Manifold Invariants held at Park City Mathematics Institute 2019, covering topics in topology, global analysis, and physics, from introductory to cutting-edge. It provides a snapshot of a vibrant and fast-moving field.

Format: Hardback
Length: 476 pages
Publication date: 01 October 2021
Publisher: American Mathematical Society

Quantum Field Theory and Manifold Invariants, a comprehensive volume, encompasses a diverse range of lectures delivered during the Graduate Summer School Quantum Field Theory and Manifold Invariants held at the Park City Mathematics Institute in 2019. These lectures span various topics, including topology, global analysis, and physics, catering to both introductory and advanced levels. The lectures delve into diverse subjects such as mathematical gauge theory, classical and categorified knot invariants, instanton Floer homology, invertible topological field theory, BPS states, and spectral networks. This collection offers a captivating blend of geometry and topology, interspersed with theoretical physics insights, providing a snapshot of a dynamic and rapidly evolving field.

This volume is particularly valuable for graduate students with a solid foundation in topology and geometry, serving as a comprehensive resource to acquire advanced background knowledge before delving into the forefront of current developments. Moreover, seasoned researchers will find this volume immensely useful as it presents a systematic overview of exciting new advancements by renowned experts in their respective fields.

The lectures in this volume are organized into four main sections. The first section focuses on mathematical gauge theory, exploring topics such as anti-self-dual equations, Seiberg-Witten equations, and Higgs bundles. These lectures provide an in-depth understanding of the fundamental principles and applications of gauge theories in physics.

The second section delves into classical and categorified knot invariants, including Khovanov homology, Heegaard Floer homology, and instanton Floer homology. These lectures offer a comprehensive exploration of knot invariants, their mathematical properties, and their connections to various branches of mathematics and physics.

The third section explores invertible topological field theory, a branch of mathematics that studies topological fields with an invertible action. These lectures introduce the concept of invertible fields, discuss their properties, and explore their applications in various areas of mathematics and physics.

The fourth section focuses on BPS states and spectral networks, which are fundamental concepts in quantum field theory. These lectures provide an introduction to BPS states, their properties, and their connections to other areas of physics, including string theory and black holes.

In conclusion, Quantum Field Theory and Manifold Invariants is a remarkable resource that offers a comprehensive and insightful exploration of various aspects of quantum field theory and its applications. Whether you are a graduate student seeking to expand your knowledge or a seasoned researcher seeking to stay updated on the latest developments, this volume is an invaluable asset.

Dimension: 254 x 178 (mm)
ISBN-13: 9781470461232