Path Integrals and Anomalies in Curved Space

An advanced introduction to a powerful method for describing quantum phenomena for researchers and graduate students.

Fiorenzo Bastianelli (Author), Peter van Nieuwenhuizen (Author)

9780521847612, Cambridge University Press

Hardback, published 20 July 2006

398 pages
25.3 x 18.2 x 2.6 cm, 0.854 kg

"Thanks to the exceptional clarity of the presentation, the meticulous attention to the subtleties of the calculations can be appreciated both by researchers who are experts in the subject and by graduate students who are approaching this field with minimum background knowledge. Anyone who is interested in this subject should read this book carefully."
Diego N. Pelliccia for Mathematical Reviews

Path integrals provide a powerful method for describing quantum phenomena. This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories. The authors start by deriving path integrals for particles moving in curved space and their supersymmetric generalizations. They then discuss the regularization schemes essential to constructing and computing these path integrals. This topic is used to introduce regularization and renormalization in quantum field theories in a wider context. These methods are then applied to discuss and calculate anomalies in quantum field theory. Such anomalies provide enormous constraints in the search for physical theories of elementary particles, quantum gravity and string theories. An advanced text for researchers and graduate students of quantum field theory and string theory, the first part is also a stand-alone introduction to path integrals in quantum mechanics.

Preface
Part I. Path Integrals for Quantum Mechanics in Curved Space: 1. Introduction to path integrals
2. Time slicing
3. Mode regularization
4. Dimensional regularization
Part II. Applications to Anomalies: 5. Introduction to anomalies
6. Chiral anomalies from susy quantum fields
7. Trace anomalies from ordinary and susy quantum mechanics
8. Conclusions and summary
Appendices A-F
References
Index.

Subject Areas: Statistical physics [PHS], Quantum physics [quantum mechanics & quantum field theory PHQ], Particle & high-energy physics [PHP]