Fermions and anomalies in quantum field theories
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Bibliographic Information
Fermions and anomalies in quantum field theories
（Theoretical and mathematical physics）
Springer, c2023
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Includs bibliographical refrence and index
Description and Table of Contents
Description
This book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories.
The book is targeted to researchers and graduate students.
Table of Contents
I. Basic tools
I Fermions
2 Classical and BRST symmetries
3 Conformal symmetry
II.
Anomalies and cohomology
4 Effective actions and anomalies
5 Cohomological analysis of
anomalies
III.
Perturbative methods for anomalies
6 Feynman diagrams and
regularizations
7 Perturbative diffeomorphism and
trace anomalies
IV.
Non-perturbative
methods. (A) heat kernel
8 Functional non-perturbative
methods
9 Explicit non-perturbative
derivations
10 Metric-axial-tensor (MAT)
background
V.
Non-perturbative
methods. (B) Index theorem
11 Geometry of anomalies
12 Anomalies as obstructions: the Atiyah-Singer family's index theorem
13 Global anomalies
VI.
Special
topics
14 MAT in 2d
15 Wess-Zumino terms
16 Sigma model anomalies
17 Anomalies and (super)string theories
by "Nielsen BookData"