Fermions and Anomalies in Quantum Field Theories

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

• Part I. Basic tools.- Chapter.1 Fermions.- Chapter 2. Classical and BRST Symmetries.- Chapter 3.Conformal symmetry.- Part II. Anomalies and cohomology.- Chapter 4.Effective actions and anomalies.- Chapter  5.Cohomological analysis of anomalies.- Part III. Perturbative methods for anomalies.- Chapter 6.Feynman diagrams and regularizations.- Chapter 7.Perturbative diffeomorphism and trace anomalies.- Part IV. Nonperturbative methods. (A) heat kernel.- Chapter 8.Functional non-perturbative methods.- Chapter 9.Explicit non-perturbative derivations.- Chapter 10.Metric-axial-tensor (MAT) background.- Part V. Nonperturbative methods. (B) Index theorem.- Chapter 11.Geometry of anomalies.- Chapter 12.Anomalies as obstructions: the Atiyah-Singer family’s index theorem.- Chapter 13.Global anomalies.- Part VI. Special topics.- Chapter 14.MAT in 2d.- Chapter 15.Wess-Zumino terms.- Chapter 16.Sigma model anomalies.- Chapter 17.Anomalies and (super)string theories.- Chapter 18. Literature and further readings.

“The topics covered are presented at a very high level in all respects. Though most of the material is well established, the book is strongly influenced by the personality of the author, including his scientific positions and preferences. … the book is a useful and valuable addition to the existing special literature on the formal aspects of modern quantum field theory.” (Ilya Shapiro, Mathematical Reviews, February, 2024)