[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"project-84190":3},{"id":4,"name":5,"fullName":6,"owner":7,"repo":5,"description":8,"homepage":8,"htmlUrl":8,"language":9,"languages":8,"totalLinesOfCode":8,"stars":10,"forks":11,"watchers":12,"openIssues":13,"contributorsCount":14,"subscribersCount":14,"size":14,"stars1d":12,"stars7d":15,"stars30d":15,"stars90d":14,"forks30d":14,"starsTrendScore":16,"compositeScore":17,"rankGlobal":8,"rankLanguage":8,"license":18,"archived":19,"fork":19,"defaultBranch":20,"hasWiki":19,"hasPages":19,"topics":21,"createdAt":8,"pushedAt":8,"updatedAt":22,"readmeContent":23,"aiSummary":8,"trendingCount":14,"starSnapshotCount":14,"syncStatus":12,"lastSyncTime":24,"discoverSource":25},84190,"QFT","xiyin137\u002FQFT","xiyin137",null,"TeX",106,9,2,36,0,8,12,48.8,"Other",false,"main",[],"2026-06-12 04:01:43","# Notes on Quantum Field Theory\n\nThis repository contains the working manuscript and project infrastructure for\na comprehensive multi-volume monograph on quantum field theory.\n\nAuthor line for the monograph:\n\n> GPT 5.5 under the supervision of Xi Yin\n\n## Complete Volume Program (I-XX)\n\nThe public monograph program consists of exactly the twenty volumes listed in\nthe table below.  Volumes I-XII are active reader-facing volumes compiled by\n`monograph\u002Ftex\u002Fmain.tex` into the current PDF.  Volumes XIII-XX are roadmap\nvolumes: they are part of the public subject architecture, and their standalone\nTeX assemblies will be added only after the same chapter-dossier,\nverification, frontmatter, and README standards are met.\n\nThis is the canonical README roster.  Do not infer the full program from\n`monograph\u002Ftex\u002Fvolumes\u002F` alone, since that directory currently contains only\nthe active compiled assemblies.  The same I--XX roster is mirrored in\n`planning\u002FREADME.md` and `planning\u002F04_master_architecture.md`.\n\n| Volume | Status | Title | Current assembly or home |\n| --- | --- | --- | --- |\n| I | Compiled | Foundations of Local Quantum Field Theory | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_i\u002Fvolume_i_current.tex` |\n| II | Compiled | Particles, Scattering, and Analyticity | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_ii\u002Fvolume_ii_current.tex` |\n| III | Compiled | Renormalization, Effective Field Theory, and Critical Phenomena | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_iii\u002Fvolume_iii_current.tex` |\n| IV | Compiled | Gauge Theory, Infrared Structure, and Anomalies | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_iv\u002Fvolume_iv_current.tex` |\n| V | Compiled | Conformal Field Theory | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_v\u002Fvolume_v_current.tex` |\n| VI | Compiled | Integrable Quantum Field Theory | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_vi\u002Fvolume_vi_current.tex` |\n| VII | Compiled | Supersymmetric Quantum Field Theory | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_vii\u002Fvolume_vii_current.tex` |\n| VIII | Compiled | Topological and Cohomological Quantum Field Theory | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_viii\u002Fvolume_viii_current.tex` |\n| IX | Compiled | Global Structure, Phases, and Extended Operators | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_ix\u002Fvolume_ix_current.tex` |\n| X | Compiled | Thermal Quantum Field Theory, Hydrodynamics, and Nonequilibrium Dynamics | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_x\u002Fvolume_x_current.tex` |\n| XI | Compiled | Constructive, Lattice, and Numerical Quantum Field Theory | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_xi\u002Fvolume_xi_current.tex` |\n| XII | Compiled | Quantum Field Theory in Curved Spacetime and Background Fields | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_xii\u002Fvolume_xii_current.tex` |\n| XIII | Roadmap | Large-N Gauge Theory, QCD Strings, Flux Tubes, Baryons, and Gauge-String Expansions | Roadmap; material presently distributed across Volumes IV, VI, VII, and IX |\n| XIV | Roadmap | Advanced Local-Algebraic QFT and Modular Structure | Roadmap; material presently distributed across Volumes I, X, XI, and XII |\n| XV | Roadmap | Advanced Scattering, Amplitudes, Resonances, and Infrared-Safe Observables | Roadmap; material presently distributed across Volumes II, IV, and V |\n| XVI | Roadmap | Advanced Supersymmetric Theories and Protected Sectors | Roadmap; material presently centered in Volume VII |\n| XVII | Roadmap | Advanced Two-Dimensional CFT and Exact Two-Dimensional QFT | Roadmap; material presently distributed across Volumes V, VI, VII, and XI |\n| XVIII | Roadmap | Advanced Constructive, Stochastic, and Rigorous Wilsonian QFT | Roadmap; material presently centered in Volume XI |\n| XIX | Roadmap | Advanced Phases, Defects, Categorical Symmetry, and Extended-Operator Theory | Roadmap; material presently distributed across Volumes VIII and IX |\n| XX | Roadmap | Advanced Curved-Background, Locally Covariant, and Semiclassical QFT | Roadmap; material presently centered in Volume XII |\n\nThe manuscript is an active draft.  The reader-facing text is in\n`monograph\u002Ftex\u002F`; planning notes, source transcriptions, and local reference\nmaterial are kept separate from the compiled monograph.\n\n## Active Compiled Volumes I-XII\n\nThe table below gives chapter ranges, chapter counts, scopes, and assembly\nfiles for the twelve launched volumes.  Chapter ranges are continuous printed\nchapter numbers, and counts are counts of printed `\\chapter` entries, not raw\n`\\input` lines.  Volume IV also inputs the spinor-convention source as a\nsection inside Chapter 40.\n\n| Volume | Chapters | Count | Title | Scope | Assembly file |\n| --- | ---: | ---: | --- | --- | --- |\n| I | 1-16 | 16 | Foundations of Local Quantum Field Theory | Local quantum data, Wightman\u002FAQFT\u002FOS\u002FKS frameworks, path integrals, spectral representations, and Green functions. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_i\u002Fvolume_i_current.tex` |\n| II | 17-29 | 13 | Particles, Scattering, and Analyticity | Haag--Ruelle scattering, LSZ, particles, spin, helicity, bound states, resonances, crossing, and dispersion theory. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_ii\u002Fvolume_ii_current.tex` |\n| III | 30-39 | 10 | Renormalization, Effective Field Theory, and Critical Phenomena | 1PI actions, counterterms, BPHZ forests, renormalized operators, RG, Wilsonian flow, scaling limits, and EFT. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_iii\u002Fvolume_iii_current.tex` |\n| IV | 40-55 | 16 | Gauge Theory, Infrared Structure, and Anomalies | Spinors, gauge fixing, BV, QED, Yang--Mills, QCD, jets, anomalies, and the Standard Model as a hybrid QFT. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_iv\u002Fvolume_iv_current.tex` |\n| V | 56-70 | 15 | Conformal Field Theory | Conformal representation theory, radial quantization, OPE, light-ray observables, 2D CFT, Liouville theory, and boundary CFT. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_v\u002Fvolume_v_current.tex` |\n| VI | 71-84 | 14 | Integrable Quantum Field Theory | Factorized scattering, Bethe ansatz, form factors, TBA, integrable RG flows, and exact two-dimensional examples. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_vi\u002Fvolume_vi_current.tex` |\n| VII | 85-101 | 17 | Supersymmetric Quantum Field Theory | Supersymmetry algebras, superfields, gauge dynamics, Seiberg--Witten theory, lower-dimensional examples, planar N=4 SYM, and localization. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_vii\u002Fvolume_vii_current.tex` |\n| VIII | 102-112 | 11 | Topological and Cohomological Quantum Field Theory | Metric independence, bordism functoriality, BF and Chern--Simons theory, cohomological theories, twists, and state-sum models. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_viii\u002Fvolume_viii_current.tex` |\n| IX | 113-123 | 11 | Global Structure, Phases, and Extended Operators | Global forms, higher-form symmetry, extended operators, confinement diagnostics, anomaly inflow, defects, and categorical symmetry. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_ix\u002Fvolume_ix_current.tex` |\n| X | 124-135 | 12 | Thermal Quantum Field Theory, Hydrodynamics, and Nonequilibrium Dynamics | KMS states, finite-temperature path integrals, Schwinger--Keldysh theory, transport, hydrodynamics, kinetic theory, and thermal gauge theory. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_x\u002Fvolume_x_current.tex` |\n| XI | 136-146 | 11 | Constructive, Lattice, and Numerical Quantum Field Theory | Constructive models, reflection positivity, continuum limits, lattice gauge theory, rigorous RG, stochastic quantization, and numerical regulators. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_xi\u002Fvolume_xi_current.tex` |\n| XII | 147-157 | 11 | Quantum Field Theory in Curved Spacetime and Background Fields | Locally covariant QFT, Hadamard states, stress tensors, Unruh and Hawking effects, index theory, microlocal methods, and semiclassical backreaction. | `monograph\u002Ftex\u002Fvolumes\u002Fvolume_xii\u002Fvolume_xii_current.tex` |\n\nThese twelve rows are the complete list of launched public volumes.  There are\nno hidden active volumes outside this roster.  Draft files, deprecated files,\nsource transcriptions, local reference files, and planning notes are not\nadditional public volumes.\n\n## Roadmap Volumes XIII-XX\n\nThe table below gives the complete current roadmap for the prospective\nvolumes after the twelve compiled volumes.  These entries are numbered so that\nthe README contains the full volume program, but their status remains\nprospective until the corresponding source assemblies exist and pass the same\nverification standards as Volumes I-XII.\n\n| Volume | Current status | Intended scope | Current compiled home |\n| --- | --- | --- | --- |\n| XIII | Prospective roadmap volume | Nonperturbative large-N limits, QCD string observables, baryons and solitons, planar versus confining string limits, and controlled bridges to gauge\u002Fstring spectral problems. | Mainly Volumes IV, VI, VII, and IX |\n| XIV | Prospective roadmap volume | Local von Neumann algebras, split property, modular inclusions, relative entropy, entanglement as an AQFT topic, superselection sectors in examples, and concrete interacting nets. | Volumes I, X, XI, and XII |\n| XV | Prospective roadmap volume | Analytic connected S-matrix elements, resonance poles and external unstable states, charged scattering beyond ordinary Haag--Ruelle, energy correlators, light-ray observables, and detector-defined inclusive observables. | Volumes II, IV, and V |\n| XVI | Prospective roadmap volume | GLSM and mirror symmetry, two-dimensional supersymmetric models, four-dimensional N=1 and N=2 dynamics, localization with regulated data, six-dimensional theories, and protected sectors. | Volume VII |\n| XVII | Prospective roadmap volume | Full and chiral CFT on Riemann surfaces, rational and non-rational examples, Liouville and Coulomb-gas residue logic, orbifolds, twist fields, sigma models, form factors, TCSA, TFFSA, and bridges to integrable and nonintegrable two-dimensional QFT. | Volumes V, VI, VII, and XI |\n| XVIII | Prospective roadmap volume | Constructive existence theorems, stochastic quantization, singular SPDEs, nonperturbative Wilsonian RG, scaling limits, and proofs connecting regulator data to local QFT frameworks. | Volume XI |\n| XIX | Prospective roadmap volume | Line, surface, and domain-wall operators; generalized global symmetry; categorical symmetry; noninvertible defects; phase diagnostics; anomaly inflow; and substantial examples. | Volumes VIII and IX |\n| XX | Prospective roadmap volume | Locally covariant QFT, microlocal methods, Hadamard renormalization, index-theoretic anomaly structure, semiclassical backreaction, and controlled curved-background examples. | Volume XII |\n\nContributors should treat the twelve active volumes as the authoritative\ncompiled manuscript and the roadmap table as the authoritative list of\nprospective subject expansions.  A prospective volume becomes an active public\ncompiled volume only after it has its own assembly file, chapter dossiers,\nverification pass, and frontmatter\u002FREADME entry.\n\n## Permanent Cross-Cutting Layer\n\nMathematical machinery and verification infrastructure are distributed through\nthe active volumes rather than being a separate numbered volume.  This layer\nincludes spinors, supergeometry, distribution theory, functional analysis,\nrigged Hilbert spaces, calculation-check scripts, finite-regulator examples,\nand proof dossiers.\n\n## Repository Layout\n\n- `monograph\u002Ftex\u002F`: reader-facing LaTeX manuscript.\n- `planning\u002F`: project constitution, rigor standards, source hierarchy,\n  and chapter dossiers.\n- `transcription\u002F`: TeX reconstruction of source lecture notes used as local\n  source material, not as reader-facing monograph prose.\n- `references\u002F`: local source and reference shelf.  PDFs, extracted text, and\n  private source files are intentionally excluded from git by `.gitignore`.\n- `tools\u002F`: build, audit, OCR, and skeleton-generation utilities.\n- `calculation-checks\u002F`: public-facing Python and Wolfram Language scripts\n  that verify convention-sensitive algebra used in the manuscript.\n- `qft_scripts\u002F`: reader-facing finite-regulator numerical demonstrations\n  such as Monte Carlo, Hamiltonian truncation, and DLCQ smoke examples.\n\n## Volume Architecture And Chapter Map\n\nThe full volume program is the twenty-volume list at the top of this README.\nThe compiled manuscript currently contains the first twelve subject volumes\nand uses continuous chapter numbering across those active volumes.\nThe chapter order below records the current contents of every launched volume,\nI--XII, and then continues with the planned subject blocks for roadmap\nVolumes XIII--XX.  The roadmap entries are not compiled chapters yet; they\nare included here so the README contains the full volume program in one\ncontinuous list.  The source directory names for Volumes I--XII are historical\nassembly locations, while the reader-facing part titles and chapter order\nbelow are the authoritative compiled-volume structure.  The frontmatter Source\nAssembly Map records how source files are assembled into the printed order.\n\n### Detailed Chapter Map\n\n1. Volume I: Foundations of Local Quantum Field Theory\n   - Starting Data for Local Quantum Field Theory\n   - Wightman Fields and Reconstruction\n   - Algebraic QFT: Local Nets and States\n   - Superselection Sectors and Locality Properties\n   - Relativistic Quantum Mechanics and Local Operator Structure\n   - Local Fields, Covariance, and Microcausality\n   - Hamiltonian Evolution and Time-Sliced Path Integrals\n   - Euclidean Correlation Functions and Gaussian Perturbation Theory\n   - Relativistic Scalar Fields and Canonical Quantization\n   - Symmetries, Noether Currents, and Stress Tensors\n   - Scalar Path Integrals and Green Functions\n   - Osterwalder--Schrader Reconstruction\n   - Kontsevich--Segal Functorial Quantum Field Theory\n   - Kallen--Lehmann Spectral Representation\n   - Perturbative Green Functions and Feynman Graphs\n   - Lorentzian Green Functions and Analytic Continuation\n2. Volume II: Particles, Scattering, and Analyticity\n   - Haag--Ruelle Scattering Theory\n   - LSZ Reduction\n   - Cross Sections, Phase Space, and Unitarity\n   - Massive Particles and Spin\n   - Massless Particles, Helicity, and Gauge Redundancy\n   - Haag--Ruelle Theory and Mathematical Scattering\n   - Local Data and Kernel Conventions\n   - Scattering Kernels, LSZ, and Cluster Decomposition\n   - Bound States from Exchange Amplitudes\n   - Resonances and Dressed Propagators\n   - Composite Bound States and Bethe--Salpeter Amplitudes\n   - Analyticity, Crossing, and Landau Singularities\n   - Partial Waves, Dispersion Relations, and High-Energy Bounds\n3. Volume III: Renormalization, Effective Field Theory, and Critical Phenomena\n   - Generating Functionals and the One-Particle-Irreducible Effective Action\n   - Renormalizability and Local Counterterms\n   - Subdivergences and Forest Formulas\n   - The 1PI Renormalization Group\n   - Renormalized Operators and Minimal Subtraction\n   - Stress Tensor Trace and Conformal Currents\n   - Wilsonian Effective Actions and Exact Cutoff Flow\n   - The Wilson-Fisher Fixed Point and Scaling Operators\n   - The Statistical Ising Model and Universality\n   - Effective Field Theories Without Poincare-Invariant UV Completion\n4. Volume IV: Gauge Theory, Infrared Structure, and Anomalies\n   - Spinor Fields, Fermionic Statistics, and Grassmann Path Integrals,\n     including Spinor and Gamma-Matrix Conventions\n   - Maxwell Theory, Constraints, and Gauge Fixing\n   - Quantum Electrodynamics and External States\n   - QED Renormalization and Electromagnetic Form Factors\n   - Infrared Divergences and Inclusive QED\n   - Classical Yang-Mills Theory and Matter Fields\n   - Lattice Yang--Mills as a Nonperturbative Formulation\n   - Gauge Fixing, Ghosts, and BRST Cohomology\n   - The BV Master Formalism for Gauge Effective Actions\n   - QCD Renormalization, Asymptotic Freedom, and Deep Inelastic Scattering\n   - Jets, Infrared-Safe Observables, and Hadronization\n   - Chiral Axial Anomalies\n   - The Schwinger Model: Two-Dimensional Quantum Electrodynamics\n   - Large-N Two-Dimensional QCD and the Light-Front Bound-State Equation\n   - The Standard Model as a Hybrid Quantum Field Theory\n   - Global Anomalies, Spontaneous Symmetry Breaking, and Pions\n5. Volume V: Conformal Field Theory\n   - Fixed Points and Conformal Data\n   - Conformal Killing Vectors and the Conformal Group\n   - Stress Tensor, Weyl Structure, and Improvement\n   - Radial Quantization and the State-Operator Correspondence\n   - Conformal Charges and Ward Identities\n   - Primary Operators and Finite Conformal Transformations\n   - Unitarity Bounds and Short Multiplets\n   - Correlation Functions and Conformal Frames\n   - The Operator Product Expansion\n   - Light-Ray Operators and Energy Correlators\n   - Two-Dimensional Sigma Models, Orbifolds, and Twist Fields\n   - Vertex Operator Algebras, Modular Sewing, and Logarithmic CFT\n   - Liouville Conformal Field Theory\n   - Boundary Conformal Field Theory\n   - Two-Dimensional Superconformal Algebras\n6. Volume VI: Integrable Quantum Field Theory\n   - Factorized Scattering and Integrability\n   - Two-Dimensional Scattering Analyticity and Bootstrap Data\n   - Yang--Baxter Consistency and Internal Symmetry\n   - Algebraic Bethe Ansatz and Transfer Matrices\n   - Nested Bethe Ansatz and Matrix Bethe--Yang Equations\n   - Form-Factor Bootstrap and Local Operators\n   - Thermodynamic Bethe Ansatz\n   - Nested TBA, Baxter Relations, and Separation Variables\n   - Integrable RG Flows and Perturbed Two-Dimensional CFT\n   - Mirror-Channel TBA and Finite-Size Effects\n   - Sine-Gordon, Massive Thirring, and Affine Toda Theories\n   - O(N), Gross--Neveu, and Sigma-Model Families\n   - Bridges to Nonintegrable Two-Dimensional QFT and CFT\n   - Finite-Volume Form Factors and Spectral Expansions\n7. Volume VII: Supersymmetric Quantum Field Theory\n   - Supersymmetry Algebras and Representation Data\n   - Superspace, Superfields, and Local Actions\n   - Supersymmetric Gauge Theory\n   - Supersymmetric Wilsonian Schemes and Exact Dynamics\n   - Nonrenormalization and Holomorphy\n   - Four-Dimensional N=1 Gauge Dynamics\n   - Four-Dimensional N=2 Gauge Dynamics and Seiberg-Witten Theory\n   - Spectral Bridges among Supersymmetric Yang--Mills Cousins\n   - Moduli Spaces in Supersymmetric Quantum Field Theory\n   - Two-Dimensional Supersymmetric Models\n   - Three-Dimensional Chern--Simons--Matter Theories\n   - Six-Dimensional Superconformal Theories\n   - Planar N=4 Supersymmetric Yang-Mills as a Spectral Problem\n   - All-Loop Asymptotic Bethe Ansatz\n   - Mirror TBA and the Y-System\n   - Quantum Spectral Curve and Hexagon Form Factors\n   - Supersymmetric Localization on Compact Manifolds\n8. Volume VIII: Topological and Cohomological Quantum Field Theory\n   - Metric Independence and Cohomological Observables\n   - Bordism Functoriality and Extended Topological Field Theory\n   - BF Theory\n   - Chern--Simons Theory\n   - Cohomological Field Theories\n   - Topological Sigma Models\n   - Twists of Supersymmetric Theories\n   - Witten-Donaldson Theory and the Seiberg-Witten Comparison\n   - Boundaries, Defects, and Categories in Topological QFT\n   - BV Integration and Finite-Dimensional Localization\n   - Finite Gauge Theory and State-Sum TQFT\n9. Volume IX: Global Structure, Phases, and Extended Operators\n   - Global Forms and Higher-Form Symmetry\n   - Extended Operators and Topological Defects\n   - Line, Surface, and Domain-Wall Operators\n   - Confinement, Screening, and Oblique Confinement\n   - Discrete Theta Terms\n   - Anomaly Inflow and Invertible Field Theories\n   - Phases of Gauge Theories\n   - Boundaries and Defects\n   - Categorical Symmetry and Defect Fusion\n   - Duality Defects, Gauging, and Orbifold Data\n   - Higher-Group Symmetry and Symmetry TQFT\n10. Volume X: Thermal Quantum Field Theory, Hydrodynamics, and Nonequilibrium Dynamics\n    - KMS States and Thermal Correlators\n    - Finite-Temperature Path Integrals\n    - Real-Time Schwinger--Keldysh Formalism\n    - Spectral Functions, Kubo Formulae, and Transport\n    - Hydrodynamics from Ward Identities\n    - Schwinger--Keldysh Hydrodynamic Effective Actions\n    - Thermal Gauge Theory and Screening\n    - Kinetic Theory as a Controlled Limit\n    - Anomalous and Topological Transport\n    - Nonequilibrium Steady States and Open-System Limits\n    - Hydrodynamic Fluctuations and Long-Time Tails\n    - QCD Phase Structure, Plasma, and Dense Matter\n11. Volume XI: Constructive, Lattice, and Numerical Quantum Field Theory\n    - Constructive Status and Routes to Continuum QFT\n    - Constructive Scalar Models and OS Data\n    - Lattice Reflection Positivity\n    - Continuum Limits and Scaling Windows\n    - Wilson Lattice Gauge Theory\n    - Monte Carlo Methods and Sign Problems\n    - Rigorous Renormalization Group\n    - Relation between Lattice and Continuum Local QFT\n    - Stochastic Quantization and Singular SPDE\n    - Hamiltonian Truncation, DLCQ, and Benchmark Protocols\n    - Lattice Fermions and Chiral Symmetry\n12. Volume XII: Quantum Field Theory in Curved Spacetime and Background Fields\n    - Locally Covariant QFT and Hadamard States\n    - Point Splitting and Stress Tensor Renormalization\n    - Trace Anomalies and Background Variations\n    - The Unruh Effect and Wedge Modular Theory\n    - The Hawking Effect\n    - Background Gauge Fields and Index Theory\n    - Eta Invariants and Global Anomalies\n    - Cosmological Spacetimes and Particle Creation\n    - Microlocal Spectrum Condition and Hadamard Geometry\n    - Perturbative Algebraic QFT on Curved Backgrounds\n    - Semiclassical Backreaction and Stress-Tensor Fluctuations\n13. Volume XIII: Large-N Gauge Theory, QCD Strings, Flux Tubes, Baryons, and Gauge-String Expansions\n    - Nonperturbative large-N limits and order-of-limits questions\n    - Wilson loops, flux tubes, and QCD string observables\n    - Baryons, solitons, and large-N scaling of multiparticle sectors\n    - Planar versus confining string limits\n    - Bridges to gauge\u002Fstring spectral problems\n14. Volume XIV: Advanced Local-Algebraic QFT and Modular Structure\n    - Local von Neumann algebras and concrete interacting nets\n    - Split property, nuclearity, and phase-space conditions\n    - Modular inclusions, relative entropy, and structural reconstruction\n    - Entanglement as an AQFT topic rather than a formal path-integral slogan\n    - Superselection sectors in substantial examples\n15. Volume XV: Advanced Scattering, Amplitudes, Resonances, and Infrared-Safe Observables\n    - Analytic connected S-matrix elements and sheet structure\n    - Resonance poles and the problem of external unstable particles\n    - Charged scattering beyond ordinary Haag--Ruelle theory\n    - Energy correlators, light-ray observables, and detector-defined inclusive data\n    - Polynomial bounds, dispersion theory, and nonperturbative amplitude constraints\n16. Volume XVI: Advanced Supersymmetric Theories and Protected Sectors\n    - Supersymmetric Wilsonian schemes and BV-compatible regulators\n    - GLSM, mirror symmetry, and two-dimensional supersymmetric models\n    - Four-dimensional N=1 and N=2 exact dynamics\n    - Localization with explicitly stated analytic and regulator hypotheses\n    - Protected sectors and higher-dimensional supersymmetric examples\n17. Volume XVII: Advanced Two-Dimensional CFT and Exact Two-Dimensional QFT\n    - Full and chiral CFT on Riemann surfaces\n    - Rational, logarithmic, and non-rational examples\n    - Liouville theory and Coulomb-gas residue logic\n    - Orbifolds, twist fields, sigma models, and conformal perturbation theory\n    - Bridges to form factors, TCSA, TFFSA, and integrable\u002Fnonintegrable 2D QFT\n18. Volume XVIII: Advanced Constructive, Stochastic, and Rigorous Wilsonian QFT\n    - Constructive existence theorems and OS\u002FWightman output maps\n    - Stochastic quantization and singular SPDE reconstruction\n    - Nonperturbative Wilsonian RG and scaling limits\n    - Proofs connecting regulator data to local QFT frameworks\n    - Examples that test the relationship among constructive, lattice, and RG routes\n19. Volume XIX: Advanced Phases, Defects, Categorical Symmetry, and Extended-Operator Theory\n    - Line, surface, and domain-wall operators\n    - Generalized global symmetry and categorical symmetry\n    - Noninvertible defects and phase diagnostics\n    - Anomaly inflow and extended-operator anomaly matching\n    - Substantial examples across gauge theory, TQFT, and CFT\n20. Volume XX: Advanced Curved-Background, Locally Covariant, and Semiclassical QFT\n    - Locally covariant QFT beyond the introductory framework\n    - Microlocal methods and Hadamard renormalization\n    - Index-theoretic anomaly structure on backgrounds\n    - Semiclassical backreaction and stress-tensor fluctuations\n    - Controlled curved-background examples and open structural problems\n\n## Build\n\nThe monograph build expects a TeX installation with `xelatex`, `latexmk`, TikZ,\nand standard AMS packages.  The strict text audit additionally requires\n`ripgrep`.\n\nFrom the repository root:\n\n```bash\ntools\u002Fbuild_monograph.sh\n```\n\nThe script runs the reader-facing text audit, builds\n`monograph\u002Ftex\u002Fmain.tex`, scans the final LaTeX logs for serious issues, and\nwrites the compiled PDF to `monograph\u002Ftex\u002Fmain.pdf`.\n\nPublic Python verification runners expect one repository-level Python\nenvironment with the numerical and HDF5 dependencies used by both\n`calculation-checks\u002F` and `qft_scripts\u002F`.  Create or refresh it with:\n\n```bash\ntools\u002Fbootstrap_verification_python.sh\n```\n\nThe runners prefer `.venv\u002Fbin\u002Fpython` when it imports the required packages.\nSet `QFT_PYTHON=\u002Fabsolute\u002Fpath\u002Fto\u002Fpython` only when using a nonstandard\nenvironment; that one interpreter is then used for ordinary Python checks and\nHDF5 checks alike.\n\nConvention-sensitive calculation checks can be run with:\n\n```bash\ntools\u002Frun_calculation_checks.sh\n```\n\nThe runner first executes the Python checks.  If `.wl` checks exist, it then\nrequires a working Wolfram backend, preferring\n`\u002FApplications\u002FWolfram.app\u002FContents\u002FMacOS\u002FWolframKernel -script` on the\nauthor's macOS installation and falling back to `wolframscript -file` only\nwhen the kernel entrypoint is unavailable.  The runner probes the selected\nbackend, runs every `.wl` file, rejects known Wolfram line-continuation parse\nhazards, and fails unless each Wolfram script prints its success marker.\nComputationally heavy or numerical checks should be implemented in Python.\nWolfram Language checks are reserved for lightweight, reader-readable symbolic\nconvention checks.  Set `QFT_SKIP_WOLFRAM=1` only for an explicitly\nPython-only pass, and set `WOLFRAMKERNEL=\u002Fabsolute\u002Fpath\u002Fto\u002FWolframKernel` or\n`WOLFRAMSCRIPT=\u002Fabsolute\u002Fpath\u002Fto\u002Fwolframscript` to override executable paths.\nThe aggregate release gate below treats the Python calculation checks as the\ncanonical mandatory evidence lane.  Wolfram Language companions are optional\nthere because the committed `.wl` files duplicate Python coverage.\n\nReader-facing companion scripts can be smoke-tested with:\n\n```bash\ntools\u002Frun_qft_scripts_smoke.sh\n```\n\nThese scripts illustrate finite regulators.  Their smoke tests do not\nestablish continuum extrapolations or physical spectra unless the\naccompanying chapter states and proves the finite claim being checked.\n\n## Quality Gates\n\nFor ordinary edit readiness, use the fast local gate:\n\n1. Run `tools\u002Fbuild_monograph.sh`.\n2. Check that the strict monograph text audit is clean.\n3. Check that the LaTeX log scan is clean.\n4. For figure-heavy edits, render and inspect the affected PDF pages.\n5. For edits involving sign, spinor, group-theory, anomaly, conformal-block,\n   or Feynman-integral conventions, run `tools\u002Frun_calculation_checks.sh` or\n   the relevant script in `calculation-checks\u002F`.\n6. For edits to public numerical companion scripts, run\n   `tools\u002Frun_qft_scripts_smoke.sh` or the edited script's smoke mode.\n\nFor a release candidate, run the aggregate local gate instead:\n\n```bash\ntools\u002Fverify_release.sh\n```\n\nThis writes timestamped JSON and Markdown manifests under\n`monograph\u002Ftex\u002Fbuild\u002Frelease_verification\u002F`, recording the Git revision and\ndirty state, tool versions, selected verification Python, mandatory audit\u002Fbuild\nresults, PDF page count and SHA-256, figure count, command logs, and skipped or\nselected optional passes.  Add\n\n```bash\ntools\u002Fverify_release.sh --rendered-figures --qft-scripts-smoke\n```\n\nwhen the release pass should also regenerate rendered figure-page artifacts and\nrun the rendered-page QA audit plus the public numerical smoke suite.  A clean\nrelease signoff should not use `--allow-dirty`; that flag is only for\ndiagnosing the gate while local edits are present.\n\nAdd `--wolfram-checks` only when the optional Wolfram Language companion lane\nshould be selected.  When selected, the verifier records the lane separately in\nthe manifest and fails if the Wolfram backend probe or any `.wl` success marker\nfails; when not selected, the manifest records an explicit optional skip.\n\nThe planning layer records additional writing standards and audit procedures.\n\n## GitHub Policy\n\nGenerated files, local build products, OCR outputs, source PDFs, and extracted\nreference text are ignored.  Compiled PDFs should be distributed through\nrelease artifacts rather than committed directly unless the author explicitly\ndecides otherwise.\n\nThe repository does not use a GitHub CI gate.  Manuscript verification is run\nlocally with the tools listed above, and `.github\u002Fworkflows\u002F` should not be\nintroduced unless the author explicitly requests GitHub Actions.\n\n## Contributing\n\nThis is an open-source project.  Contributions should be made by pull request,\nand every pull request must be reviewed and approved by Xi Yin or by a\nmaintainer explicitly designated by Xi Yin before it is merged.  See\n`CONTRIBUTING.md` for the manuscript-quality, verification, and licensing\nexpectations.\n\n## License\n\nSee `LICENSE` for the mixed licensing terms: manuscript and scholarly content\nunder CC BY 4.0, executable code under MIT.\n","2026-06-11 04:12:31","CREATED_QUERY"]