Statistical Approach to Quantum Field Theory: An Introduction

Tian Yu Cao

Introduction: Conceptual issues in quantum field theory Part I. Philosophers' Interests in Quantum Field Theory: 1. Why are we philosophers interested in quantum field theory 2. Quantum field theory and the philosopher Part II. Three Approaches to the Foundations of Quantum Field Theory: 3. The usefulness of a general theory of quantized fields 4. Effective field theory in condensed matter physics 5. The triumph and limitations of quantum field theory 6. Comments Discussions Part III. Does Quantum Field Theory Need a Foundation: 7. Does quantum field theory need a foundation? Part IV. Mathematics, Statistical Mechanics and Quantum Field Theory: 8. Renormalization group theory: its basis and formulation in statistical physics 9. Where does quantum field theory fit into the big picture? 10. The unreasonable effectiveness of quantum field theory 11. Comment: the quantum field theory of physics and of mathematics Part V. Quantum Field Theory and Spacetime: Introduction 12. Quantum field theory and spacetime: formalism and reality 13. Quantum field theory of geometry 14. 'Localization' in quantum field theory: how much of QFT is compatible with what we know about spacetime 15. Comments VI. 16. What is quantum field theory and what did we think it was? 17. Comments Discussions Part VII.Renormalization Group: 18. What is fundamental physics? A renormalization group perspective 19. Renormalization group: an interesting yet puzzling idea Part VIII. Non-Abelian Gauge Theory: 20. Gauge fields, gravity and Bohm's theory 21. Is the Aharonov-Bohm effect local? Discussions Part IX. The Ontology of Particles or Fields: 22. The ineliminable classical face of quantum field theory 23. The logic of quanta 24. Do Feynman diagrams endorse a particle ontology? 25. On the ontology of QFT Part X. Panel Discussion.

Andreas Wipf

Efim S. Fradkin, Igor Anatol'evich Batalin, G. A. Vilkovisky +1 more

Giuseppe Mussardo

Abstract This book is an introduction to statistical field theory, which is an important subject within theoretical physics and a field that has seen substantial progress in recent years. The book covers fundamental topics in great detail and includes areas like conformal field theory, quantum integrability, S-matrices, braiding groups, Bethe ansatz, renormalization groups, Majorana fermions, form factors, the truncated conformal space approach and boundary field theory. It also provides an introduction to lattice statistical models. Many topics are discussed at a fairly advanced level but via a pedagogical approach. In particular, the book presents in a clear way non-perturbative methods of quantum field theories that have become decisive tools in many different areas of statistical and condensed matter physics, and which are currently an essential foundation of the working knowledge of a modern theoretical physicist.

Vladimir V. Bazhanov, Conrad J. Burden

General principles of statistical mechanics, P.A. Pearce the connection between statistical mechanics and quantum field theory, B.M. McCoy two-dimensional models in statistical mechanics, R.J. Baxter topics in conformal field theory, C. Itzykson quantum gravity as dynamical triangulation, A.A. Migdal lattice gauge theory, C.J. Hamer quantum groups for physicists, M. Gould chaos versus order in Hamiltonian dynamical systems, G.R.W. Quispel quantum and classical integrable systems and statistical mechanics, R.K. Bullough and J.T. Timonen introduction to quantum field theory, R.J. Crewther.

Ragnheidur Gudmundsdóttir