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
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
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 Toward a Mathematical Theory of Social Fields First Edition (2026) Author: Chou I-Hsien Dedication To those who believe that mathematics is not merely a collection of formulas, but a language through which the hidden structures of reality may gradually be revealed. To every mathematician who has sought unity beneath diversity, to every physicist who has transformed geometry into dynamics, to every computer scientist who has discovered structure within information, to every philosopher who has pursued clarity through logic, and to every student who has dared to ask why seemingly unrelated phenomena often obey remarkably similar mathematical principles — this work is respectfully dedicated. The development of mathematics has always depended upon imagination disciplined by rigor. Every new mathematical language begins with a simple question: can apparently different systems be understood through the same underlying structure? This question inspired analytic geometry, calculus, group theory, differential geometry, Hilbert spaces, information theory, and category theory. It is the same question that motivates the present work. Social Quantum Field Theory is offered not as the final answer, but as one possible step toward a broader mathematical synthesis. If future generations discover that many of its ideas are incomplete, they should improve them. If some ideas are incorrect, they should replace them. If entirely better formulations emerge, they should be embraced without hesitation. Such is the natural evolution of mathematics. No mathematical framework belongs permanently to its first author. Every worthwhile theory eventually becomes part of a larger intellectual tradition, refined through criticism, generalization, and collaboration across generations. The greatest hope for this work is therefore not that it remains unchanged, but that it becomes unnecessary — because future mathematicians will have constructed something even more elegant upon its foundations. May this book encourage its readers to value rigor over rhetoric, structure over appearance, proof over assertion, curiosity over certainty, and understanding over complexity. For mathematics advances not by defending established ideas, but by continually discovering deeper patterns that unite what once appeared separate. "The pursuit of structure is the pursuit of understanding." Dedicated to all researchers who seek unity through mathematics, and all future scholars who will carry that search further.
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.
Quantum field theory is a powerful language for the description of the subatomic constituents of the physical world and the laws and principles that govern them. This book contains up-to-date in-depth analyses, by a group of eminent physicists and philosophers of science, of our present understanding of its conceptual foundations, of the reasons why this understanding has to be revised so that the theory can go further, and of possible directions in which revisions may be promising and productive. These analyses will be of interest to graduate students and research workers in physics who want to know about the foundational problems of their subject. The book will also be of interest to professional philosophers, historians and sociologists of science, because it contains much material for metaphysical and methodological reflections, for historical and cultural analyses, and for sociological analyses of the way in which various factors contribute to the way the foundations are revised.
Ediverso Theory: A Unified Theory of Possibility, Choice and Reality Ediverso Theory proposes a new mathematical and conceptual framework for describing how realities emerge from fields of admissible possibilities. While classical mathematics, logic and physics primarily study realised states, determined values and observed outcomes, Ediverso Theory introduces possibility itself as a fundamental object of formal investigation. The framework is built upon four primitive concepts: Possibility (E) — the field of admissible states; Choice (Ω) — the operator that transforms possibility into reality; Memory (H) — the accumulated history of realised states; Coherence (C) — the structure that constrains consistent evolution. From these primitives emerges a unified formal architecture spanning geometry, topology, information theory, observer theory, computational systems, physics, logic, mathematics, consciousness, evolution and collective dynamics. At the core of the theory lies the Ediverso operator: ╠╬╣ which represents a structured field of admissible possibilities rather than a single realised value. Classical mathematics appears as a limiting case when the possibility field collapses to a single point. The work develops: • A Geometry of Possibility• A Topology of Admissible Realities• An Information Theory of Choice• A Formal Theory of Observers• Computational Ediverso Systems for Artificial Intelligence• Possibility-Based Physical Models• Ediverso Logic and Mathematical Foundations• Theories of Consciousness, Evolution and Civilizational Dynamics• The Irreducibility Theorem of Ediverso Systems The central question motivating the entire research programme is: What exists before reality becomes reality? Rather than treating possibility as ignorance, uncertainty or incomplete information, Ediverso Theory investigates the hypothesis that possibility possesses its own independent mathematical structure and that reality emerges through admissible selection within that structure. This manuscript presents the first complete formulation of the Ediverso Research Program and is intended as an open scientific framework subject to mathematical analysis, criticism, refinement, extension and falsification. If successful, Ediverso Theory may provide a common language for describing decision, emergence, information, observation and reality across disciplines traditionally studied in isolation. Reality is not the beginning. Reality is the consequence. Possibility is the beginning. Keywords: Ediverso Theory, Possibility Mathematics, Choice Theory, Emergence, Information Theory, Observer Theory, Mathematical Foundations, Logic, Artificial Intelligence, Consciousness Studies, Complexity Science, Theoretical Physics, Philosophy of Mathematics, Foundations of Reality.
Preface Part I. Quantum Mechanics: 1. On the low density of Boson models: Langevin equation L. Accardi and L. Y. Gang 2. Schrodinger operators with potentials supported by null sets S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, W. Karwowski and T. Lindstrom 3. Landau Hamiltonians on symmetric spaces J. E. Avron and A. Pnueli 4. Renormalization group analysis and quasicrystals J. Bellissard 5. The measurement problem in the stochastic formulation of quantum mechanics Ph. Blanchard, M. Cini and M. Serva 6. Schrodinger operators at threshold D. Bolle 7. Spectral analysis and scattering theory for Schrodinger operators with an interaction supported by a regular curve J. F. Brasche and A. Teta 8. Lattice models of solids V. V. Evstratov and B. S. Pavlov 9. Schrodinger operators on unusual manifolds P. Exner and P. Seba 10. High energy resolvent estimates for Schrodinger operators A. Jensen 11. Point interactions as solvable models W. Kirsch 12. Stochastic model of quantum mechanics V. P. Maslov Part II. Quantum Field Theory: 13. Maximality of infinite dimensional Dirichlet forms and Hoegh-Krohn's model of quantum fields S. Albeverio and S. Kusuoka 14. Global Markov property in quantum field theory and statistical mechanics: a review on results and problems S. Albeverio and B. Zegarlinski 15. Hypercontractivity: a bibliographic review E. B. Davies, L. B. Gross and B. Simon 16. Progress and problems in algebraic quantum field theory S. Doplicher 17. Hoegh-Krohn's model of quantum fields and the absolute continuity of measures S. Kusuoka 18. Baryon states in lattice QCD R. A. Minlos and E. A. Zhinzhina 19. The energy of a Weyl soliton R. F. Streater Part III. Statistical Physics: 20. Morphology and classification of galaxies: a stochastic model S. Albeverio, Ph. Blanchard, D. Gandolfo, R. Hoegh-Krohn and M. Mebkhout 21. Thermodynamic inequalities for the surface tension and the geometry of the Wulff construction R. L. Dobrushin and S. B. Shlosman 22. Verification of the global Markov property for strongly coupled trigonometric interactions R. Gielerak 23. Decomposition of Ising models and the Mayer expansion C. M. Newman and G. A. Baker, Jr 24. Towards time-dynamics for bosonic systems in quantum statistical mechanics A. G. Shuhov, Yu. M. Suhov and A. V. Teslenko 25. Towards time-dynamics for bosonic systems in quantum statistical mechanics, 2 A. G. Shuhov and Yu. M. Suhov.