Daniel S. Freed's Books

Five Lectures on Supersymmetry

By: Daniel S. Freed

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Five Lectures on Supersymmetry

By: Daniel S. Freed

The lectures featured in this book treat fundamental concepts necessary for understanding the physics behind these mathematical applications. Freed approaches the topic with the assumption that the basic notions of supersymmetric field theory are unfamiliar to most mathematicians. He presents the material intending to impart a firm grounding in the elementary ideas.

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Page Count

132

Publisher

American Mathematical Soc.

ISBN 10

0821871935

ISBN 13

9780821871935

Instantons and Four-Manifolds

By: Daniel S. Freed,Karen K. Uhlenbeck

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Instantons and Four-Manifolds

By: Daniel S. Freed,Karen K. Uhlenbeck

From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate... The book is filled with insightful remarks, proofs, and contributions that have never before appeared in print. For anyone attempting to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology, the book is a must." #Science#1 "I would strongly advise the graduate student or working mathematician who wishes to learn the analytic aspects of this subject to begin with Freed and Uhlenbeck's book." #Bulletin of the American Mathematical Society#2

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Page Count

212

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461397030

ISBN 13

9781461397038

Topology and Quantum Theory in Interaction

By: David Ayala,Daniel S. Freed,Ryan E. Grady

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Topology and Quantum Theory in Interaction

By: David Ayala,Daniel S. Freed,Ryan E. Grady

This volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31–August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme Segal. Papers contained in this volume amplify various aspects of the Freed–Hopkins program, develop some category theory, which lies behind the cobordism hypothesis, the major structure theorem for topological field theories, and relate to Costello's approach to perturbative quantum field theory. Two papers on the latter use this framework to recover fundamental results about some physical theories: two-dimensional sigma-models and the bosonic string. Perhaps it is surprising that such sparse axiom systems encode enough structure to prove important results in physics. These successes can be taken as encouragement that the axiom systems are at least on the right track toward articulating what a quantum field theory is.

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Page Count

274

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470442434

ISBN 13

9781470442439

Geometry and Quantum Field Theory

By: Daniel S. Freed,Karen K. Uhlenbeck

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Geometry and Quantum Field Theory

By: Daniel S. Freed,Karen K. Uhlenbeck

Exploring topics from classical and quantum mechnanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come.

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Page Count

472

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821804006

ISBN 13

9780821804001

Lectures on Field Theory and Topology

By: Daniel S. Freed

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Lectures on Field Theory and Topology

By: Daniel S. Freed

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

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Page Count

202

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470452065

ISBN 13

9781470452063

Quantum Field Theory, Supersymmetry, and Enumerative Geometry

By: Daniel S. Freed,David R. Morrison,Isadore Manuel Singer

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Quantum Field Theory, Supersymmetry, and Enumerative Geometry

By: Daniel S. Freed,David R. Morrison,Isadore Manuel Singer

This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Supersymmetry, and Enumerative Geometry. With this volume, the Park City Mathematics Institute returns to the general topic of the first institute: the interplay between quantum field theory and mathematics.

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Page Count

297

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821834312

ISBN 13

9780821834312

Book's by Daniel S. Freed

Five Lectures on Supersymmetry

Five Lectures on Supersymmetry

Instantons and Four-Manifolds

Instantons and Four-Manifolds

Topology and Quantum Theory in Interaction

Topology and Quantum Theory in Interaction

Geometry and Quantum Field Theory

Geometry and Quantum Field Theory

Lectures on Field Theory and Topology

Lectures on Field Theory and Topology

Quantum Field Theory, Supersymmetry, and Enumerative Geometry

Quantum Field Theory, Supersymmetry, and Enumerative Geometry

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