Landau, Lifshitz — *The Classical Theory of Fields* (Fast Track 1.03) — Audit + Gap Plan

Book: L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, Volume 2 of the Course of Theoretical Physics. Canonical English edition: 4th revised English edition, translated by Morton Hamermesh, Butterworth-Heinemann / Pergamon, 1975 (reprinted with corrections through the 1980s and 1990s; ISBN 0-7506-2768-9). Russian original 1st edition 1939 (Landau and Lifshitz); the 7th Russian edition (1988) is the basis of the 4th revised English. 402 pages, 14 chapters.

Fast Track entry: 1.03 of docs/catalogs/FASTTRACK_BOOKLIST.md, the SR + EM + GR slot of the Course of Theoretical Physics strand. Sibling entry 1.02 Mechanics (Landau Vol 1) is being audited in parallel this cycle and is a hard prerequisite for the Lagrangian-mechanics framing that opens Vol 2.

Purpose: lightweight audit-and-gap pass (P1-lite + P2 + P3-lite of the orchestration protocol in docs/plans/AGENTIC_EXECUTION_PLAN.md). Output is a concrete punch-list of new units to write so that Classical Theory of Fields (CTF hereafter) is covered to the equivalence threshold (≥95% effective coverage; see docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md §3.4).

Audit completeness: reduced per AGENTIC_EXECUTION_PLAN §6.6. The PDF is not in the local reference/ archive and is BUY-only (Pergamon / Butterworth-Heinemann holds rights; no author-hosted PDF, no public-domain Internet Archive scan accessible at audit time). The §1 inventory below is built from the publicly visible Elsevier / ScienceDirect TOC, peer references (MTW, Jackson, Wald, Carroll), and the citation network. P5 verification on this audit cannot mark CTF equivalence-covered; only equivalence-partial until re-audited from a full source. Re-audit upgrade queued in docs/catalogs/NEED_TO_SOURCE.md.

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§1 What CTF is for

CTF is the second volume of the Landau-Lifshitz Course of Theoretical Physics. It is the canonical physicist's exposition of classical field theory: the entire content of special relativity, classical electrodynamics, and general relativity is derived inside ~400 pages from a single editorial premise — the principle of least action applied to fields and to point particles coupled to fields. The book is the Landau-school distillation: definitions are minimal, derivations proceed by physical reasoning rather than by mathematical formalism, and every field theory in the book (the free relativistic particle, the electromagnetic field, the gravitational field) is introduced as the simplest action invariant under the relevant symmetry group.

Distinctive editorial framing, in roughly the order CTF develops it:

1. Relativity principle first. Chapter 1 begins not with Maxwell's equations and an asymmetry in their transformation laws (Einstein 1905, Jackson Ch. 11) but with the Einstein-synchronisation construction of the invariant interval $d{s}^2=c^{2}d{t}^2-d{x}^2-d{y}^2-d{z}^2$ as a postulate. The Lorentz group is then derived as the isometry group of $d{s}^2$. This is the inverse of the historical / Jackson order and is pedagogically decisive: every later chapter is "what is the simplest action invariant under the Poincaré group?".

2. Relativistic mechanics as a one-line action principle (Ch. 2). The free-particle action is $S=-mc\int ds$ — the unique Poincaré-invariant functional linear in proper time. From it the entire kinematics (four-momentum, $E=m{c}^2$, mass-shell condition) drops out by variation. Compare Jackson §12.1 (postulates Maxwell, derives Lorentz) and Goldstein Ch. 7 (Lagrangian first but no field-theoretic continuation): only LL takes the action functional as primary and carries it forward to EM and GR.

3. EM as the simplest field theory of a vector potential coupled to particles (Ch. 3-4). The interaction term $-(e/c)\int A_{\mu }d{x}^{\mu }$ is the unique Poincaré- and gauge-invariant coupling linear in $A_{\mu }$. The free-field term $-(1/16\pi c) \int F_{\mu\nu} F^{\mu\nu} , d^4 x$ is the unique gauge-invariant Lorentz scalar quadratic in $\partial A$. Maxwell's equations are then Euler-Lagrange equations from the total action. Compare Jackson Ch. 11-12: Jackson postulates Maxwell and checks covariance; LL postulates covariance and derives Maxwell.

4. Gravity as the geometric field theory on Lorentzian manifolds (Ch. 10-11). The gravitational field is identified with the spacetime metric $g_{\mu \nu }$; the equivalence principle is the postulate that in a freely falling frame all non-gravitational physics reduces to special relativity. The geodesic equation is then the EL equation of $-mc\int ds$ on a curved Lorentzian background. The Einstein-Hilbert action $S_g=-(c^3/16\pi G)\int R\sqrt{-g}{d}^{4}x$ is the simplest scalar invariant built from the metric and its derivatives, and Einstein's equations $G_{\mu \nu }=(8\pi G/c^4)T_{\mu \nu }$ are its EL equations. This is the Hilbert 1915 derivation in a physicist's idiom, presented as the obvious continuation of the EM construction.

5. Energy-momentum and stress-energy tensors as Noether currents (Ch. 4 and 11). The canonical stress-energy tensor for EM is constructed directly from translation invariance of the action; the Hilbert stress-energy tensor for matter is the source of Einstein's equations, defined by $T_{\mu\nu} = -(2 / \sqrt{-g}) \delta S_m / \delta g^{\mu\nu}$. The two definitions are reconciled via improvement terms (Belinfante-Rosenfeld), though LL does not emphasise the symmetrisation problem explicitly.

6. Explicit solutions ahead of formalism. CTF computes the Schwarzschild and Reissner-Nordström solutions (Ch. 12), the Friedmann-Lemaître cosmologies (Ch. 14), the Liénard-Wiechert potentials and synchrotron radiation (Ch. 8-9) all in coordinate formulas without committing to a coordinate-free differential-geometric treatment. Compare Wald and Carroll, which set up the coordinate-free machinery first; LL goes directly from $g_{\mu \nu }$ in coordinates to the Schwarzschild metric.

7. Compactness and selection. ~400 pages cover what MTW (1279 pp.), Jackson (832 pp.) and Wald (491 pp.) cover combined. The selection is consciously physicist's: no formal differential geometry, no bundle-theoretic gauge framing, no causal-structure theorems (Penrose-Hawking singularity theory is mentioned only in passing in §14). The trade-off is loss of mathematical generality in exchange for derivational unity across SR + EM + GR.

8. Pointer to QFT (Ch. 4, 11, 14). The action-principle framing continues into Vol 4 (Quantum Electrodynamics) and is the reason CTF is the natural pre-text for a path-integral course. CTF stops at the classical level — quantisation is Vol 4's job — but the editorial choice of the action functional is exactly what makes the quantisation programme transparent.

CTF is not a first introduction to electromagnetism or to relativity for the mathematically untrained: there is essentially no exterior calculus (forms appear only implicitly as antisymmetric tensors), no formal differential geometry beyond index notation, and limited rigorous treatment of distributions or weak solutions. It assumes Vol 1 Mechanics (Lagrangian and Hamiltonian formalism on $TQ$ and $T^{\ast }Q$) and undergraduate vector calculus + linear algebra. The canonical alternative texts — cited throughout the §1 inventory and as audit cross-checks — are:

• C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, W. H. Freeman 1973. (MTW.) The encyclopaedic differential-geometric treatment of GR; Track-1 / Track-2 structure mirrors CTF's physicist-first approach but with a coordinate-free language layer CTF lacks.
• J. D. Jackson, Classical Electrodynamics, 3rd edition, Wiley 1998. The encyclopaedic EM reference. Jackson postulates Maxwell and derives covariance; CTF inverts this order.
• R. M. Wald, General Relativity, University of Chicago Press 1984. The canonical mathematically-rigorous GR text; covers causal-structure theory, singularity theorems, and asymptotic structure that CTF omits. Wald is the bridge between CTF's physicist GR and the Lorentzian-geometry literature.
• S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Pearson 2003. Modern pedagogical GR; covers differential-geometric prerequisites in Ch. 2-3 in a style closer to the Codex's existing 03-modern-geometry/ strand than LL's index calculus.

A fifth optional cross-check, useful for the EM-as-gauge-theory bridge that CTF foreshadows but does not develop, is B. Felsager, Geometry, Particles, and Fields, Springer 1998 — the same content in fibre-bundle language.

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§2 Coverage table (Codex vs CTF)

Cross-referenced against the current 313-unit corpus (manifests/ inventory at audit time). ✓ = covered, △ = partial / different framing, ✗ = not covered.

CTF chapter / topic	Codex unit(s)	Status	Note
Ch. 1 — Principle of relativity; Lorentz transformations; invariant interval	05.00.06-galilean-newtonian-setup (Galilean limit only); 04.05.09-hodge-index-theorem (mentions Minkowski signature in algebraic-geometry analogy)	△	Gap. Minkowski space, Lorentz group, invariant interval, four-vectors are not first-class objects. Galilean-Lorentzian contraction is mentioned in passing in 05.00.06 line 218 but not developed.
Ch. 2 — Relativistic mechanics; four-momentum; mass-shell; $E=m{c}^2$	—	✗	Gap. Free relativistic particle action $S=-mc\int ds$ is not in the Codex. 05.00.04-noether-theorem has a ${\mathbb{R}}^4$ scalar-field example with Lagrangian density but no relativistic point particle.
Ch. 3 — Charges in EM fields; gauge invariance; field-particle interaction	03.04.08-variational-calculus (covers EL on fibre bundles, abstractly); 05.00.04-noether-theorem (covers Noether currents abstractly)	△	Gap. No unit treats the EM 4-potential $A_{\mu }$, the field tensor $F_{\mu \nu }$, or the minimal coupling $-(e/c)A_{\mu }d{x}^{\mu }$ explicitly.
Ch. 4 — EM field equations; Maxwell's equations from action; stress-energy	03.07.05-yang-mills-action (abelian case is EM, but framed as gauge theory not as CTF builds it); 05.00.04-noether-theorem (line 273 has scalar-field stress-energy example)	△	Gap. Maxwell's equations from $-(1/16\pi c)\int F_{\mu \nu }{F}^{\mu \nu }{d}^{4}x$, the EM stress-energy tensor in physicist's index notation, Poynting vector, and conservation laws are not directly covered.
Ch. 5 — Constant EM fields; Coulomb law; magnetic dipole; multipole expansion	—	✗	Gap. Standard EM problems (point charge, dipole, multipole) absent from Codex.
Ch. 6 — Electromagnetic waves; plane waves; polarisation; energy flux	—	✗	Gap. Plane-wave solutions of Maxwell, polarisation, wave-zone fields absent.
Ch. 7 — Propagation of light; geometric optics; eikonal; Doppler; aberration	—	✗	Gap. Eikonal limit, light-cone propagation, optical phenomena absent.
Ch. 8 — Field of moving charges; Liénard-Wiechert potentials; retarded potentials	—	✗	Gap. Retarded Green's function, Liénard-Wiechert formulas absent.
Ch. 9 — Radiation of EM waves; Larmor formula; multipole radiation; synchrotron	—	✗	Gap. Larmor formula, multipole radiation, accelerated-charge spectrum absent.
Ch. 10 — Particle in a gravitational field; metric tensor; geodesic equation; equivalence principle	05.02.06-geodesic-flow-hamiltonian (Riemannian geodesic flow as a Hamiltonian system; not Lorentzian, no equivalence-principle framing)	△	Gap. Lorentzian metric, equivalence principle, Christoffel symbols, geodesic equation as EL of $-mc\int ds$ on curved background are not in the Codex. Riemannian (positive-definite) geodesic flow is covered; the Lorentzian extension is not.
Ch. 11 — Gravitational field equations; Riemann curvature; Einstein-Hilbert action	03.05.09-curvature (curvature of a connection on a vector bundle; pure mathematical setup); 03.07.05-yang-mills-action (action principle for gauge connections, abelian and non-abelian; not metric-based)	△	Gap. Riemann curvature of a Lorentzian metric, Ricci tensor and Ricci scalar, Bianchi identities, Einstein-Hilbert action $S=-(c^3/16\pi G)\int R\sqrt{-g}{d}^{4}x$, and the Einstein field equations $G_{\mu \nu }=8\pi G{T}_{\mu \nu }/c^4$ are not in the Codex. The Codex has connection-curvature for vector bundles but not the Levi-Civita connection of a Lorentzian metric and its specific curvature tensors.
Ch. 12 — Field of gravitating bodies; Schwarzschild; Reissner-Nordström; Kerr	—	✗	Gap. No exact solutions of Einstein's equations.
Ch. 13 — Gravitational waves; weak-field limit; quadrupole formula	—	✗	Gap. Linearised gravity, transverse-traceless gauge, quadrupole radiation formula absent.
Ch. 14 — Relativistic cosmology; FLRW; Friedmann equations; cosmological constant	—	✗	Gap. Cosmological solutions, scale factor, redshift, $\Lambda$CDM are absent.

Aggregate coverage estimate: ~5-10% of CTF has corresponding or neighbouring Codex units; the rest is uncovered. The Codex has the mathematical infrastructure for several CTF chapters (variational calculus on bundles, abstract Noether theorem, abstract curvature of a connection, Riemannian geodesic flow) but none of the physical content in CTF's framing — neither special relativity, nor Maxwell theory, nor general relativity have dedicated units. Closing this is a substantial new-unit punch-list. The Vol 1 Mechanics punch-list is a strict prerequisite for the relativistic-mechanics units (3 + 4 below).

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§3 Gap punch-list (P3-lite — units to write, priority-ordered)

The natural Codex location for CTF content is a new sub-strand within 03-modern-geometry/ (provisionally 03.14-relativity/ or 03.15-classical-field-theory/ — directory name to be confirmed during P3 setup against docs/specs/UNIT_SPEC.md's strand convention) for SR and GR, and a new top-level dossier within 05-symplectic/ or the new field-theory strand for the EM content. Numbering below uses placeholder XX.YY.NN pending strand assignment in P3.

Priority 0 — blocked by Vol 1 Mechanics punch-list: The relativistic-mechanics units (3, 4 below) require Vol 1 priority-1 units on the action principle for a single particle, four-velocity vs. three-velocity, and the canonical correspondence between Galilean and Newtonian mechanics. Vol 1 audit is running in parallel this cycle; check plans/fasttrack/landau-mechanics.md (sibling audit) for the exact blocker list before scheduling Priority-1 production.

Priority 1 — high-leverage, captures CTF's editorial core (SR + EM action principle + GR action principle):

1. XX.YY.01 Minkowski space and the Lorentz group. ${\mathbb{R}}^{1,3}$ with signature $(+,-,-,-)$ (CTF / particle-physics convention; cross-walk to the $(-,+,+,+)$ convention used in parts of 03-modern-geometry/ recorded explicitly — see §4), invariant interval $d{s}^2$, Lorentz transformations as $\mathrm{O}(1,3)$, Poincaré group as the affine extension. Wikipedia / MTW Ch. 1-3 / Carroll §1 cross-check. Three-tier. Beginner: $1+1$ Lorentz boost, time dilation, length contraction. Intermediate: full ${\mathrm{SO}}^{+}(1,3)$ structure, generators, Lie algebra. Master: bridge to spin geometry (03.09.02-clifford-algebra already records the LL signature convention conflict, line 658) and to the existing Galilean-contraction note in 05.00.06-galilean-newtonian-setup. ~1800 words.

2. XX.YY.02 Four-vectors, four-tensors, and the index calculus on ${\mathbb{R}}^{1,3}$. $x^{\mu }$ vs $x_{\mu }$, raising and lowering with ${\eta }_{\mu \nu }$, summation convention, ${\partial }_{\mu }$ vs ${\partial }^{\mu }$, antisymmetric tensors and the dual via ${ϵ}^{\mu \nu \rho \sigma }$. Pure notation unit, ~1200 words. Beginner only. CTF Ch. 1 §6 anchor; Jackson §11.6 cross-check.

3. XX.YY.03 The relativistic free-particle action $S=-mc\int ds$. CTF Ch. 2 §8. Derivation of four-momentum $p^{\mu }=(E/c,\mathbf{p})$, mass-shell $p^{\mu }{p}_{\mu }=m^2{c}^2$, $E^2=(pc{)}^2+(m{c}^2{)}^2$, the non-relativistic limit. Three-tier. Master section: the action as the simplest Poincaré-invariant functional linear in proper time (uniqueness up to total derivative). ~2000 words. Bridges Vol 1 Lagrangian-mechanics priority-1 unit; the action principle generalises 05.00.02-hamilton-principle to the relativistic case.

4. XX.YY.04 Charged particle in an EM field: minimal coupling. CTF Ch. 3 §16. The interaction action $-(e/c)\int A_{\mu }d{x}^{\mu }$ as the unique gauge-invariant scalar linear in $A_{\mu }$, the Lorentz force law $d{p}^{\mu }/d\tau =(e/c)F^{\mu \nu }{u}_{\nu }$ as the EL equation, the field tensor $F_{\mu \nu }={\partial }_{\mu }{A}_{\nu }-{\partial }_{\nu }{A}_{\mu }$, gauge transformations $A_{\mu }\to A_{\mu }+{\partial }_{\mu }\chi$. Three-tier. Master section: bridge to 03.05.07-principal-bundle-connection — the $A_{\mu }$ is the local form of a $U(1)$-connection on a principal bundle over Minkowski space. ~2200 words.

5. XX.YY.05 The EM field action and Maxwell's equations. CTF Ch. 4 §27. The free-field action $-(1/16\pi c) \int F_{\mu\nu} F^{\mu\nu} , d^4 x$ as the unique gauge-invariant Lorentz scalar quadratic in $\partial A$, the EL equations $\partial_\mu F^{\mu\nu} = (4\pi/c) j^\nu$ (the inhomogeneous Maxwell equations), the Bianchi identity ${\partial }_{\mu }{F}^{\ast }{}^{\mu \nu }=0$ (the homogeneous Maxwell equations). Three-tier. Master section: comparison with the abelian case of Yang-Mills (03.07.05-yang-mills-action) and the bundle-theoretic re-derivation. ~2500 words. Originator-prose anchor — Maxwell 1865 / 1873 Treatise on Electricity and Magnetism and Einstein 1905 Annalen der Physik as the citation pair.

6. XX.YY.06 Stress-energy tensor of the EM field. CTF Ch. 4 §32-33. Canonical $T^{\mu \nu }$ from translation invariance via Noether's theorem on a Lagrangian density (extending 05.00.04-noether-theorem's field-theory addendum), symmetrisation problem, the symmetric $T^{\mu\nu} = -F^{\mu\alpha} F^\nu{}\alpha + (1/4) \eta^{\mu\nu} F^{\alpha\beta} F{\alpha\beta}$,conservation$\partial_\mu T^{\mu\nu} = 0$, Poynting vector and energy flux. Three-tier. ~2000 words.

7. XX.YY.07 Lorentzian metric and the equivalence principle. CTF Ch. 10 §82, §87. A Lorentzian manifold $(M,g)$ with signature $(+,-,-,-)$, the equivalence principle as the postulate that locally inertial frames reduce all non-gravitational physics to SR, Christoffel symbols ${\Gamma }_{\mu \nu }^{\lambda }$ as the unique torsion-free metric-compatible connection, the geodesic equation $\ddot x^\lambda

   • \Gamma^\lambda_{\mu\nu} \dot x^\mu \dot x^\nu = 0$ as the EL of $-mc\int ds$ on $(M,g)$. Three-tier. Master section: bridge to 05.02.06-geodesic-flow-hamiltonian (the Riemannian-positive case) and to 03.05.07-principal-bundle-connection (the Levi-Civita connection as a specific principal-bundle connection on the orthonormal frame bundle, which is 03.05.03-orthogonal-frame-bundle adapted to Lorentzian signature). ~2500 words.

8. XX.YY.08 Riemann curvature, Ricci tensor, scalar curvature on a Lorentzian manifold. CTF Ch. 11 §91-92. Riemann tensor $R^{\rho }{}_{\sigma \mu \nu }$ in coordinates, symmetries (antisymmetry in first and second pairs, pair-symmetry, first Bianchi), Ricci tensor $R_{\mu \nu }=R^{\rho }{}_{\mu \rho \nu }$, scalar curvature $R = g^{\mu\nu} R_{\mu\nu}$,secondBianchiidentity$\nabla_\lambda R^\rho{}_{\sigma\mu\nu}

   • \nabla_\mu R^\rho{}{\sigma\nu\lambda} + \nabla\nu R^\rho{}_{\sigma\lambda\mu} = 0$. Three-tier. Master section: bridge to 03.05.09-curvature (curvature of a connection on a vector bundle; the Lorentzian Riemann tensor is a specific case for the Levi-Civita connection on $TM$). ~2200 words.

9. XX.YY.09 The Einstein-Hilbert action and the Einstein field equations. CTF Ch. 11 §93. The action $S_g = -(c^3 / 16\pi G) \int R \sqrt{-g} , d^4 x$ as the simplest scalar invariant of the metric and its derivatives, derivation of the EL equation $G_{\mu\nu} = R_{\mu\nu}

   • (1/2) g_{\mu\nu} R = (8\pi G / c^4) T_{\mu\nu}$, the Hilbert stress-energy tensor $T_{\mu\nu} = -(2 / \sqrt{-g}) \delta S_m / \delta g^{\mu\nu}$. Three-tier. Master section: originator-prose treatment citing Hilbert 1915 Die Grundlagen der Physik and Einstein 1915 Sitzungsberichte (independent discovery); the Hilbert variational derivation is the editorial centre of LL Ch. 11. ~2800 words.

Priority 2 — completes CTF's worked-solutions and radiation chapters:

10. XX.YY.10 Liénard-Wiechert potentials and retarded Green's function. CTF Ch. 8 §62-66. The retarded Green's function for the d'Alembertian, the Liénard-Wiechert potentials of a moving point charge. Three-tier. ~2000 words. Jackson §14 cross-check.

11. XX.YY.11 Larmor formula and multipole radiation. CTF Ch. 9 §67-71. Power radiated by an accelerated charge, dipole and quadrupole radiation, the radiation reaction problem (Abraham-Lorentz). Three-tier. ~2000 words. Jackson §9, §16 cross-check.

12. XX.YY.12 Schwarzschild solution. CTF Ch. 12 §97. Spherically symmetric vacuum solution of Einstein's equations, the Schwarzschild coordinates, the event horizon at $r=2GM/c^2$, perihelion advance and light bending. Three-tier. ~2500 words. Wald Ch. 6, MTW §31, Carroll Ch. 5 cross-check.

13. XX.YY.13 Linearised gravity and the quadrupole formula. CTF Ch. 13 §107. Weak-field $g_{\mu \nu }={\eta }_{\mu \nu }+h_{\mu \nu }$, the transverse-traceless gauge, the wave equation $\Box \bar h_{\mu\nu} = -(16\pi G / c^4) T_{\mu\nu}$,thequadrupoleformula$P = (G / 5c^5) \langle \dddot Q_{\mu\nu} \dddot Q^{\mu\nu} \rangle$. Three-tier. ~2000 words. MTW §35, Wald §4.4 cross-check.

14. XX.YY.14 FLRW cosmology and Friedmann equations. CTF Ch. 14 §111-112. The FLRW metric with scale factor $a(t)$, the two Friedmann equations as Einstein's equations on the FLRW ansatz, redshift, cosmological constant. Three-tier. ~2000 words. Wald §5, Carroll Ch. 8 cross-check.

Priority 3 — Master-tier deepenings and constant-field / wave chapters (complete CTF's EM coverage to ≥95%):

15. XX.YY.15 Plane EM waves and polarisation. CTF Ch. 6 §47-50. Pointer or short unit; bridges to optics units in future strands. ~1200 words.

16. XX.YY.16 Geometric optics and the eikonal equation. CTF Ch. 7 §53. Pointer unit. ~1000 words.

17. XX.YY.17 Constant fields: Coulomb law, dipole, multipole. CTF Ch. 5 §36-41. Pointer / refresher unit. ~1500 words.

Priority 4 — survey pointers (optional, Master-only):

18. XX.YY.18 Causal structure and singularity theorems. Pointer unit at FT-equivalence. Wald Ch. 8-9, Penrose-Hawking, Hawking-Ellis Large Scale Structure of Space-Time as bibliography. CTF mentions only in passing. ~1200 words.

19. XX.YY.19 Kerr and Reissner-Nordström solutions. Pointer unit; CTF Ch. 12 §104. ~1200 words.

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§4 Implementation sketch (P3 → P4)

For a full CTF coverage pass, items 1-9 are the minimum set (with the Vol 1 priority-1 prereqs as a strict requirement). Realistic production estimate, mirroring earlier batches:

• ~3.5-4.5 hours per CTF unit. CTF units skew higher than the corpus average because (a) the index calculus is unfamiliar to the Codex's current differential-geometry idiom, (b) master tier requires explicit cross-walks to bundle-theoretic framings already in 03-modern-geometry/, and (c) physical interpretation paragraphs beyond the mathematical statements add length to every tier.
• 9 priority-1 units × ~4 hours = ~36 hours of focused production. Plus the Vol 1 priority-1 prereqs (estimate from sibling audit). Plus priority-2 (5 units × ~4 hours = ~20 hours) to close the EM and GR worked-solutions / cosmology gap. Total ~56 hours of CTF-specific production, fitting a focused 8-10 day window. Priority-3+4 are Master-tier deepenings and can ship later.

Originator-prose targets. CTF is itself an expository text (Landau school distillation), not the original source for any of the theorems it develops. The originator citations for priority-1 units 5 and 9 should trace through CTF back to:

• J. C. Maxwell, A Treatise on Electricity and Magnetism, Vols I-II, Oxford 1873 — the original Maxwell-equations text. Used for unit 5 (the EM field equations).
• A. Einstein, "Zur Elektrodynamik bewegter Körper," Annalen der Physik 17 (1905) 891-921 — special relativity. Used for unit 1.
• A. Einstein, "Die Feldgleichungen der Gravitation," Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin, 25 Nov 1915) 844-847 — the Einstein field equations. Used for unit 9.
• D. Hilbert, "Die Grundlagen der Physik," Nachrichten von der Königl. Gesellschaft der Wissenschaften zu Göttingen (20 Nov 1915) 395-407 — the variational derivation of the field equations from the Einstein-Hilbert action, which is CTF's framing. Used for unit 9.
• E. Noether, "Invariante Variationsprobleme," Nachr. d. Kgl. Ges. d. Wiss. zu Göttingen (1918) 235-257 — the conserved-currents theorem; already cited from 05.00.04-noether-theorem, re-cited for unit 6.

Notation crosswalk (load-bearing for this strand). CTF uses the $(+,-,-,-)$ Minkowski signature (timelike $+$, spacelike $-$), greek indices $\mu ,\nu ,\dots$ for 4-tensors and latin indices $i,j,\dots$ for 3-tensors, the Einstein summation convention, and the ${\eta }_{\mu \nu }=\mathrm{diag}(+1,-1,-1,-1)$ metric.

The Codex's existing 03-modern-geometry/ strand uses $(-,+,+,+)$ in several places — 03.09.02-clifford-algebra line 658 explicitly records the LM (Lawson-Michelsohn) convention as $(-,+,+,+)$ in the spin-geometry treatment, and notes "the physics literature works in Lorentzian signature $(1,3)$ with the opposite sign convention from LM." The 03.09.04-spin-structure and 03.09.05-spinor-bundle units inherit the LM $(-,+,+,+)$ convention.

This is a direct conflict between the LL convention used in the new CTF strand and the LM convention used in the existing spin-geometry strand. The convention decision is:

• Adopt the CTF $(+,-,-,-)$ signature inside the new XX.YY.NN-* units (priority-1 units 1-9 and priority-2 units 10-14). This is the physicist's convention; CTF's index calculus is unworkable in $(-,+,+,+)$ without rewriting every signed term, and the audience for this strand is reading the Landau-school programme directly.
• Document the conflict explicitly in a §Notation paragraph of unit 1 (XX.YY.01 Minkowski space and the Lorentz group) and unit 7 (XX.YY.07 Lorentzian metric and the equivalence principle), citing 03.09.02-clifford-algebra and noting that the spin-geometry units use the opposite signature. Any unit that lateral-connects to a spin-geometry unit must include a one-line signature crosswalk.
• Record in docs/specs/UNIT_SPEC.md §11 notation conventions (P2 task) as a strand-level decision: SR/EM/GR units inherit CTF signature; spin-geometry / Lorentzian-Dirac units inherit LM signature; cross-strand bridges include explicit signature crosswalks. This is the same pattern 03.09.02 already establishes in its physics-vs-LM crosswalk, generalised to the new strand.

Without this decision being recorded explicitly, P4 (units-cross-link) will produce broken citation chains in the spin-geometry-to-relativity bridge units (most notably any unit on the Dirac equation on a Lorentzian manifold, which sits exactly at the conflict).

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§5 What this plan does NOT cover

• A line-number-level inventory of every named formula in CTF (full P1 audit; deferred to a future re-audit once the PDF is sourced — see AGENTIC_EXECUTION_PLAN §6.6 hard rule).
• Exercise-pack production. CTF problems are extensive (~30-50 per chapter, ~500 total) and frequently open-ended; exercise pack is a P3-priority-3 follow-up after the priority-1 units ship and the full-source re-audit is complete. (Reduced-audit constraint: §1.2 exercise inventory is omitted per AGENTIC_EXECUTION_PLAN §6.6.)
• The Yang-Mills non-abelian generalisation of EM. CTF's EM-action framing extends naturally to Yang-Mills, but Yang-Mills as a curriculum strand is anchored at FT 3.20 Atiyah Geometry of Yang-Mills Fields (and to 03.07.05-yang-mills-action, already in the Codex), not at FT 1.03. Defer the non-abelian gauge content to the Atiyah and Donaldson-Kronheimer punch-lists, with a one-paragraph bridge in unit 5's Master section.
• Quantisation of any field theory. CTF stops at the classical level. Path-integral quantisation lives in the QFT track (05.00.04-noether-theorem already foreshadows it for scalar fields; full path-integral coverage is in FT 2.20 QED and the stat-mech strand 08.07.01-path-integral).
• Causal structure, singularity theorems, asymptotic structure. These are CTF-adjacent but not in CTF; bibliography pointer in priority-4 unit 18 only. Wald Ch. 8-9 is the canonical entry point.
• Numerical relativity, post-Newtonian expansion, gravitational-wave data analysis. Out of FT 1.03 scope.
• Plasma physics, magnetohydrodynamics, optical media (dispersive EM). Out of scope; Landau Vol 8 Electrodynamics of Continuous Media is the next text in the series and would be a separate Fast Track entry if added (not currently listed).

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§6 Acceptance criteria for FT equivalence (CTF)

Per docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md §3.4, the book is at equivalence-coverage when:

• The Vol 1 Mechanics priority-1 units have shipped (strict prereq for units 3, 4 — the action-principle framing).
• ≥95% of CTF's named theorems / formula-derivations across Ch. 1-14 map to Codex units. Currently ~5-10%; after priority-1 (units 1-9) this rises to ~55-60% (covers SR foundations, EM action principle, GR action principle but not all worked solutions); after priority-1+2 (adding units 10-14) to ~85% (adds Liénard-Wiechert, Larmor, Schwarzschild, linearised gravity, FLRW); full ≥95% requires priority-3 (constant fields, plane waves, eikonal — units 15-17).
• ≥90% of CTF's worked computations in Ch. 1-14 have a direct unit or are referenced from a unit covering them. The Liénard-Wiechert, Larmor, Schwarzschild, linearised-gravity, and FLRW worked computations are load-bearing for this criterion and are all in priority-2.
• Notation decisions are recorded in docs/specs/UNIT_SPEC.md §11 (see §4 above).
• Pass-W weaving connects the new units to 03-modern-geometry/ (curvature, principal-bundle connection, frame bundle, spin geometry), to 05-symplectic/lagrangian-mechanics/ (action principle, Noether), and to 03.07.05-yang-mills-action (EM as abelian gauge theory) via lateral connections.

Hard rule (AGENTIC_EXECUTION_PLAN §6.6): because this is a reduced-audit book, P5 verification cannot mark CTF equivalence-covered. The best mark achievable while the audit is reduced is equivalence-partial. To upgrade to full equivalence-cover, a full re-audit from the PDF is required and queued in docs/catalogs/NEED_TO_SOURCE.md (see §7).

The 9 priority-1 units close CTF's editorial-core coverage gap given the Vol 1 prereqs are in place. Priority-2 closes the worked-solutions gap. Priority-3+4 are deepenings and pointer-only material.

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§7 Sourcing

• BUY-only. Pergamon / Butterworth-Heinemann holds the rights for the English-language Course of Theoretical Physics; no author-hosted PDF, no free legal Internet Archive scan, no publisher preview beyond the ScienceDirect chapter list. The Russian original (Nauka) is also copyrighted.
• Canonical English edition for citation. L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, 4th revised English edition, trans. Morton Hamermesh, Course of Theoretical Physics Vol. 2, Butterworth-Heinemann 1975, ISBN 0-7506-2768-9, xv + 402 pp.
• Russian-edition citation (Vol 2 in the Teoreticheskaya Fizika series). L. D. Landau, E. M. Lifshitz, Teoriya polya, 7th edn, Nauka, Moscow 1988.
• Acquisition action. Add CTF to docs/catalogs/NEED_TO_SOURCE.md with priority: medium-high (this audit is reduced, blocking full equivalence-cover) and acquisition_paths: purchase | university ILL | institutional ScienceDirect access. Once acquired, file under reference/fasttrack-texts/03-physics/Landau-Lifshitz-Vol2-ClassicalTheoryOfFields.pdf (directory to be created if absent) and trigger a full P1 re-audit upgrade — replace this reduced audit's §1.2 (exercises) with the full inventory, recompute coverage and acceptance thresholds, and flip audit_completeness: reduced → full in manifests/production/plan.json and in manifests/campaign.json.
• Peer cross-checks used during the reduced audit (and the canonical cross-check texts to cite in the new units' tier anchors):
  • C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, W. H. Freeman 1973. Used for GR units 7-9, 12-14.
  • J. D. Jackson, Classical Electrodynamics, 3rd edn, Wiley 1998. Used for EM units 4-6, 10-11, 15-17.
  • R. M. Wald, General Relativity, University of Chicago Press 1984. Used for GR units 7-14, 18-19.
  • S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Pearson 2003. Used as the modern pedagogical cross-check for units 1, 7-14.
  • (Optional, for the bundle-theoretic bridge.) B. Felsager, Geometry, Particles, and Fields, Springer 1998. Used for the Master-tier bridges in units 4 and 5.