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OverviewThese 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. Full Product DetailsAuthor: Daniel S. Freed , Daniel S FreedPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.360kg ISBN: 9781470452063ISBN 10: 1470452065 Pages: 186 Publication Date: 30 August 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction Bordism and topological field theories Quantum mechanics Wick-rotated quantum field theory and symmetry Classification theorems Extended locality Invertibility and stable homotopy theory Wick-rotated unitarity Extended positivity and stable homotopy theory Non-topological invertible field theories Computations for electron systems Anomalies in field theory Review of categories Bibliography Index.ReviewsAuthor InformationDaniel S. Freed, University of Texas at Austin, TX. Tab Content 6Author Website:Countries AvailableAll regions |