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Lectures on Field Theory and Topology (CBMS Regional Conference Series in Mathematics) (CBMS Regional Conference Series in Mathematics, 133) free ebook download

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Author(s):	Daniel S. Freed

Date:	2024	Format:	pdf	Language:	English	ISBN/ASIN:	1470452065
Pages:	186	OCR:		Quality:		ISBN13:
Uploader:	maveriks	Upload Date:	2/12/2024 1:07:13 AM

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1470452065 pdf
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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Tags: CBMS CBMS Conference Field Lectures Mathematics Regional Regional Theory Topology

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Lectures on Field Theory and Topology (CBMS Regional Conference Series in Mathematics) (CBMS Regional Conference Series in Mathematics, 133) free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics