Softcover ISBN:  9781470452063 
Product Code:  CBMS/133 
List Price:  $58.00 
MAA Member Price:  $52.20 
AMS Member Price:  $46.40 
eBook ISBN:  9781470453916 
Product Code:  CBMS/133.E 
List Price:  $58.00 
MAA Member Price:  $52.20 
AMS Member Price:  $46.40 
Softcover ISBN:  9781470452063 
eBook: ISBN:  9781470453916 
Product Code:  CBMS/133.B 
List Price:  $116.00 $87.00 
MAA Member Price:  $104.40 $78.30 
AMS Member Price:  $92.80 $69.60 
Softcover ISBN:  9781470452063 
Product Code:  CBMS/133 
List Price:  $58.00 
MAA Member Price:  $52.20 
AMS Member Price:  $46.40 
eBook ISBN:  9781470453916 
Product Code:  CBMS/133.E 
List Price:  $58.00 
MAA Member Price:  $52.20 
AMS Member Price:  $46.40 
Softcover ISBN:  9781470452063 
eBook ISBN:  9781470453916 
Product Code:  CBMS/133.B 
List Price:  $116.00 $87.00 
MAA Member Price:  $104.40 $78.30 
AMS Member Price:  $92.80 $69.60 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 133; 2019; 186 ppMSC: Primary 55; 81; 82; 57
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.
ReadershipGraduate students and researchers interested in the interation between geometry, topology (homotopy theory), and theoretical physics (quantum field theory and condensed matter theory).

Table of Contents

Chapters

Introduction

Bordism and topological field theories

Quantum mechanics

Wickrotated quantum field theory and symmetry

Classification theorems

Extended locality

Invertibility and stable homotopy theory

Wickrotated unitarity

Extended positivity and stable homotopy theory

Nontopological invertible field theories

Computations for electron systems

Anomalies in field theory

Review of categories


Additional Material

Reviews

This book is an excellent resource both as an introduction to TQFTs as well as a guide to getting one's hands dirty with computation. I recommend it highly.
Jonathan Campbell, Center for Communications Research, La Jolla


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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.
Graduate students and researchers interested in the interation between geometry, topology (homotopy theory), and theoretical physics (quantum field theory and condensed matter theory).

Chapters

Introduction

Bordism and topological field theories

Quantum mechanics

Wickrotated quantum field theory and symmetry

Classification theorems

Extended locality

Invertibility and stable homotopy theory

Wickrotated unitarity

Extended positivity and stable homotopy theory

Nontopological invertible field theories

Computations for electron systems

Anomalies in field theory

Review of categories

This book is an excellent resource both as an introduction to TQFTs as well as a guide to getting one's hands dirty with computation. I recommend it highly.
Jonathan Campbell, Center for Communications Research, La Jolla