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
Volume 1: Introduction P. Humphreys. Part I: Probability. Some Contributions to Formal Theory of Probability K. Popper, D. Miller. Elementary Non-Archimedean Representations of Probability for Decision Theory and Games P.J. Hammond. Random Sequences and Hypotheses Tests R. Chuaqui. Changing Probability Judgements I. Levi. Upper and Lower Probability T.L. Fine. Some Connections between Epistemic Logic and the Theory of Nonadditive Probability P. Mongin. On the Properties of Conditional Independence W. Spohn. Qualitative Probabilities Revisited Z. Domotor. The Monks' Vote: a Dialogue on Unidimensional Probabilistic Geometry J.-C. Falmagne. Part II: Probabilistic Causality. Probabilistic Causation without Probability P.W. Holland. Causal Tendency, Necessitivity and Sufficientivity: an Updated Review I.J. Good. Practical Causal Generalizations E.W. Adams. In Place of Regression C. Glymour, P. Spirtes, R. Scheines. Testing Probabilistic Causality D. Costantini. Psychologistic Aspects of Suppes' Definition of Causality P. Legrenzi, M. Sonino. Name Index. Subject Index. Volume 2: Part III: Philosophy of Physics. Probability and Quantum Theory B. Loewer. Schrodinger's Version of EPR, and its Problems A. Fine. Classical Field Magnitudes J. Vuillemin. Quantity, Representation and Geometry B. Mundy. Numerical Experimentation P. Humphreys. Part IV: Theory Structure. Theories and Theoretical Models R. Wojcicki. Suppes Predicates and the Construction of Unsolvable Problems in the Axiomatized Sciences N.C.A. da Costa, F.A. Doria. Structural Explanation J.D. Sneed. Part V: Measurement Theory. Fifteen Problems concerning the Representational Theory of Measurement R.D. Luce, L. Narens. The Meaningfulness of Ordinal Comparisons for General Order Relational Systems F.S. Roberts, Z.S. Rosenbaum. Theories as Nets: the Case of Combinatorial Measurement Theory C.U. Moulines, J.A. Diez. Name Index. Subject Index. Volume 3: Part VI: Philosophy of Language and Logic. Patrick Suppes' Contribution to the Philosophy of Language D. Follesdal. Open Problems in Relational Grammar M. Bottner. A Variable-Free Logic for Anaphora W.C. Purdy. Is Snow White? J. Moravcsik. Can there be Reasons for Putting Limitations on Classical Logic? P. Weingartner. Quantum Logic as a Logic of Identification J. Hintikka, I. Halonen. Logic and Probability in Quantum Mechanics M.L. dalla Chiara, R. Giuntini. Part VII: Learning Theory, Action Theory, and Robotics. From Stimulus-Sampling to Array-Similarity Theory W.K. Estes. Action as Seeing to it that Something is the Case R. Tuomela, G. Sandu. Command Satisfaction and the Acquisition of Habits C. Crangle. Part VIII: General Philosophy of Science. Some Observations on Patrick Suppes' Philosophy of Science M.C. Galavotti. Epilogue. Postscript P. Suppes. Chronological and Topical Bibliography of Patrick Suppes' Publications. Name Index. Subject Index.
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.
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 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.