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Advanced introduction to a powerful method for describing quantum phenomena for researchers and graduate students.
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.
Table of contents:
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.
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.
Table of contents:
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.