Geometric Quantum Field Theories

Yi, Piljin

Cambridge University Press（2026/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 640 p.
• 言語 ENG
• 商品コード 9781009575560

Full Description

This graduate-level volume is a coherent and self-contained introduction to Quantum Field Theory, uniquely focused on geometric and non-perturbative aspects. The first part covers quantum fields and Euclidean path integral, Yang-Mills field theories, and Wilsonian renormalization. Wilson's notion of the effective field theory and its heavy implication for the QFT framework itself are given particular attention. Next, geometrical and topological aspects are thoroughly treated, accompanied by a healthy dose of underlying mathematics. Anomalies, or quantum failures of classical symmetries, follow as crucial litmus tests for self-consistency, which are delineated in unprecedented detail, spanning decades of development. In the final part, the book asks how relativistic gravity, known to resist standard quantization schemes, may reconcile with the quantum world. This question is approached by invoking d=2 Weyl anomaly, Hawking effects, black hole partition functions, and the renormalization of fundamental strings, with a view toward quantum gravity and superstring theory.

Contents

Part I. Quantum Fields in Brief: 1. Quantum Fields and Path Integrals; 2. Euclidean Path Integrals; 3. Running Gauge Couplings; 4. Making Sense of Quantum Field Theories; Part II. More on Gauge Theories: 5. Geometry and Topology of Gauge Fields; 6. Lie Algebra for Gauge Theories; 7. Yang-Mills Instantons; 8. More Topological Saddles; Part III. Symmetries and Anomalies; 9. Gauge Symmetries and BRST; 10. Anomalies of Continuous Symmetries; 11. More on Continuous Anomalies; 12. Discrete Anomalies; Part IV. Anomalies and Spacetimes: 13. Path Integrals in Curved Spacetime; 14. Spacetime Gravity from Strings; 15. Toward Superstrings; Appendix A. Constrained Dynamics; Appendix B. Differential Geometry 101; Appendix C. Maurer-Cartan and Spinors; Appendix D. Algebraic Topology.