Fermions and Anomalies in Quantum Field Theories

ISBN-13: 9783031219276 / Angielski / Twarda / 2023 / 434 str.

L. M. Bonora

Opis

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.

Spis treści

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

O autorze

Loriano Bonora has been Professor of Field Theory at the International School for Advanced Studies (SISSA), Trieste, Italy.