The methods of quantum field theory underpin many conceptual advances in contemporary condensed matter physics and neighbouring fields. This book provides a praxis-oriented and pedagogical introduction to quantum field theory in many-particle physics, emphasizing the application of theory to real physical systems. This third edition is organized into two parts: the first half of the text presents a streamlined introduction, elevating readers to a level where they can engage with contemporary research literature, from the introduction of many-body techniques and functional integration to renormalization group methods, and the second half addresses a range of advanced topics including modern aspects of gauge theory, topological and relativistic quantum matter, and condensed matter physics out of thermal equilibrium. At all stages, the text seeks a balance between methodological aspects of quantum field theory and practical applications. Extended problems with worked solutions provide a bridge between formal theory and a research-oriented approach.
Volume I: Foundations and Formalism (Chapters 1–10) Volume II: Information Geometry, Dynamics and Applications (Chapters 11–19) Volume III: Advanced Theory, Control, Inverse Problems and Praxis (Chapters 20–52) Chapter 1 Introduction ............................................................................... 1 Chapter 2 From Bourdieu’s Field Theory to Social Quantum Field Theory .......... xx Chapters 3–10 Axioms, Hilbert Space, Field Operators, Geometry, Renormalization, etc. Chapter 11 Information Geometry and Relational Entropy .............................. xx Chapters 12–19 Emergence, Verification, Applications, Computation & Unification Chapter 20 Quantization of Social Fields ..................................................... xx Chapter 21 Interaction Vertices and Perturbation Theory ............................... xx Chapter 22 Spontaneous Symmetry Breaking and Emergent Order ..................... xx Chapters 23–30 Critical Phenomena, Topology, Information Geometry, Networks Chapter 31 Optimal Control and Decision Theory .......................................... xx Chapter 32 Inverse Social Field Theory ....................................................... xx Chapters 33–52 Praxis: Cultivation, Institutions, AI, Geopolitics, Taiwan Cases, Philosophy & Synthesis Epilogue .............................................................................................. xx Postscript Reflections on Mathematical Modeling ....................................... xx Afterword Mathematical Vision of Social Reality ......................................... xx Appendices (L–W, X, Y, etc.) Mathematical Notation · Complete Axioms · Illustrations · Glossary · FAQs · Open Problems · Future Research Agenda References ........................................................................................... xx Index ................................................................................................. xx
Social Quantum Field Theory First Edition (2026) Table of Contents Volume I: Foundations and Formalism (Chapters 1–10) Volume II: Information Geometry, Dynamics and Applications (Chapters 11–19) Volume III: Advanced Theory, Control, Inverse Problems and Praxis (Chapters 20–52) Chapter 1 Introduction ............................................................................... 1 Chapter 2 From Bourdieu’s Field Theory to Social Quantum Field Theory .......... xx Chapters 3–10 Axioms, Hilbert Space, Field Operators, Geometry, Renormalization, etc. Chapter 11 Information Geometry and Relational Entropy .............................. xx Chapters 12–19 Emergence, Verification, Applications, Computation & Unification Chapter 20 Quantization of Social Fields ..................................................... xx Chapter 21 Interaction Vertices and Perturbation Theory ............................... xx Chapter 22 Spontaneous Symmetry Breaking and Emergent Order ..................... xx Chapters 23–30 Critical Phenomena, Topology, Information Geometry, Networks Chapter 31 Optimal Control and Decision Theory .......................................... xx Chapter 32 Inverse Social Field Theory ....................................................... xx Chapters 33–52 Praxis: Cultivation, Institutions, AI, Geopolitics, Taiwan Cases, Philosophy & Synthesis Epilogue .............................................................................................. xx Postscript Reflections on Mathematical Modeling ....................................... xx Afterword Mathematical Vision of Social Reality ......................................... xx Appendices (L–W, X, Y, etc.) Mathematical Notation · Complete Axioms · Illustrations · Glossary · FAQs · Open Problems · Future Research Agenda References ........................................................................................... xx Index ................................................................................................. xx