Lectures on Field Theory and Topology
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-5206-3 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5206-3 (ISBN)
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.
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.
Daniel S. Freed, University of Texas at Austin, TX.
Introduction
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.
| Erscheinungsdatum | 15.09.2019 |
|---|---|
| Reihe/Serie | CBMS Regional Conference Series in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 360 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-4704-5206-5 / 1470452065 |
| ISBN-13 | 978-1-4704-5206-3 / 9781470452063 |
| Zustand | Neuware |
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