Syllabus
Purpose and audience
This graduate course studies Migdal’s geometric-QCD proposal through explicit calculations and critical source reconstruction. Students should know graduate quantum field theory, gauge invariance, and elementary linear algebra and geometry. Prior expertise in loop calculus, free-word algebras, minimal surfaces, or twistors is not assumed.
The course is organized around what can be reconstructed from the page. Students learn both the proposed chain of ideas and how to test its mathematical premises.
Prerequisites and bridges
Before Module I, review matrix traces, Euclidean gamma algebra, and Gaussian integrals. Before Module II, review Fourier transforms, distributions, and row reduction. Before Module III, review differential forms, complex Fourier modes, and boundary-value problems. Before Module IV, review Grassmann Gaussian integrals and integration by parts. Before Module V, review variational calculus, induced metrics, and stationary phase.
The bridge notes supply worked examples and diagnostic answers. Students should complete the corresponding diagnostic before the first meeting of each module.
Learning outcomes
Students will derive the regulated loop insertion and color splitting; calculate finite Fourier and closure identities; distinguish ordered integrals from logarithmic Magnus terms; test consistency by ranks and certificates; construct harmonic disk maps and check conformality; calculate finite Pfaffians and a normalized contact limit; integrate a two-loop beta function; and derive and test a stationary Regge parametrization.
They will also identify the boundary between these calculations and the unresolved source claims: the full eighth-order MLE computation, the extended geometric tensor and its variational consequences, the continuum Majorana construction, exact WKB, and the global meson fit.
Full route: ten weeks, 60 contact hours
Each module takes two weeks with eight 90-minute meetings: seven mini-lectures and one written problem clinic. Four meetings per week give six contact hours.
| Weeks | Module | Lectures | Clinic focus |
|---|---|---|---|
| 1–2 | I | I.1–I.7 | Color splitting and the contact prescription |
| 3–4 | II | II.1–II.7 | A complete finite rank certificate |
| 5–6 | III | III.1–III.7 | Circle, ellipse, and extended tensor checks |
| 7–8 | IV | IV.1–IV.7 | Pfaffian, kernel normalization, RG sign |
| 9–10 | V | V.1–V.7 | Stationary phase and a fit-audit design |
The lectures total minutes, or 52.5 hours. The five clinics total 7.5 hours. The complete schedule is 60 contact hours, plus approximately 70–105 hours of independent work. These are planning estimates, not measured classroom times.
Survey route: five weeks, 25 meetings
This is a shorter survey, with one 90-minute meeting per weekday: 37.5 contact hours. It does not schedule 35 full lectures in 25 slots.
| Week | Five classroom notes | Assigned self-study notes |
|---|---|---|
| 1 | I.1, I.2, I.3, I.4, I.5 | I.6, I.7 |
| 2 | II.1, II.3, II.4, II.5, II.6 | II.2, II.7 |
| 3 | III.1, III.2, III.3, III.5, III.7 | III.4, III.6 |
| 4 | IV.1, IV.2, IV.3, IV.6, IV.7 | IV.4, IV.5 |
| 5 | V.1, V.2, V.4, V.6, V.7 | V.3, V.5 |
Assigned notes supply prerequisites for later classroom work: in particular read III.6 before V.2 and V.3 before V.4. The instructor uses the first ten minutes of each relevant meeting to check that bridge. Research extensions are optional and the full source reconstruction is not all presented in class.
Assessment
Use the instructor guide: five simultaneous short written checks, selected self-study calculations, and one concise source-audit report. Suggested weights are 40%, 30%, and 30%, respectively. Written corrections or retakes use the same rubric. No oral probing is required.
Core marks reward a defined problem, correct calculation, conventions and units, and a conclusion limited to the evidence. Research reports are graded for method and scope, not for obtaining the source author’s preferred conclusion. The instructor remains responsible for evaluating correctness; AI-assisted drafts require the same checks as other drafts.
Readiness
The revised notes and reproducible examples are teaching materials. The unresolved scientific claims are identified within them. Human reading, timed rehearsal, and feedback from students remain necessary to assess pacing and learning.