Ideal for researchers and graduate students at the interface between mathematics and physics, this text develops quantum field theory from the ground up using a rich mix of modern mathematics. It provides a unified approach to deformation quantization, Hochschild homology, vertex algebras, conformal field theory, quantum groups, and gauge theory.
Ideal for researchers and graduate students at the interface between mathematics and physics, this text develops quantum field theory from the ground up using a rich mix of modern mathematics. It provides a unified approach to deformation quantization, Hochschild homology, vertex algebras, conformal field theory, quantum groups, and gauge theory.
Kevin Costello is Krembil William Rowan Hamilton Chair in Theoretical Physics at the Perimeter Institute for Theoretical Physics, Waterloo, Canada. He is an honorary member of the Royal Irish Academy and a Fellow of the Royal Society. He has won several awards, including the Berwick Prize of the London Mathematical Society (2017) and the Eisenbud Prize of the American Mathematical Society (2020).
Inhaltsangabe
1. Introduction and overview Part I. Classical Field Theory: 2. Introduction to classical field theory 3. Elliptic moduli problems 4. The classical Batalin-Vilkovisky formalism 5. The observables of a classical field theory Part II. Quantum Field Theory: 6. Introduction to quantum field theory 7. Effective field theories and Batalin-Vilkovisky quantization 8. The observables of a quantum field theory 9. Further aspects of quantum observables 10. Operator product expansions, with examples Part III. A Factorization Enhancement of Noether's Theorem: 11. Introduction to Noether's theorems 12. Noether's theorem in classical field theory 13. Noether's theorem in quantum field theory 14. Examples of the Noether theorems Appendix A. Background Appendix B. Functions on spaces of sections Appendix C. A formal Darboux lemma References Index.
1. Introduction and overview Part I. Classical Field Theory: 2. Introduction to classical field theory 3. Elliptic moduli problems 4. The classical Batalin-Vilkovisky formalism 5. The observables of a classical field theory Part II. Quantum Field Theory: 6. Introduction to quantum field theory 7. Effective field theories and Batalin-Vilkovisky quantization 8. The observables of a quantum field theory 9. Further aspects of quantum observables 10. Operator product expansions, with examples Part III. A Factorization Enhancement of Noether's Theorem: 11. Introduction to Noether's theorems 12. Noether's theorem in classical field theory 13. Noether's theorem in quantum field theory 14. Examples of the Noether theorems Appendix A. Background Appendix B. Functions on spaces of sections Appendix C. A formal Darboux lemma References Index.
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