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ASDVariational response of the chosen coupling
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Variational response of the chosen coupling

Follows from the chosen minimal coupling; it is not used to prove the origin of the LVE magnetic correction.

Theory · DERIVEDEquation version 1.0.0

Based on the final manuscript · Chapter 3

ASD-WEB-EM-022
p˙i=q[−∂iΦτ−∂tAi+vj(∂iAj−∂jAi)],p˙=q(E+v×B)\dot p_i=q[-\partial_i\Phi_\tau-\partial_t A_i+v_j(\partial_i A_j-\partial_j A_i)],\quad\dot{\mathbf p}=q(\mathbf E+\mathbf v\times\mathbf B)

Follows from the chosen minimal coupling; it is not used to prove the origin of the LVE magnetic correction.
Chapter reference: Final collected manuscript · Chapter 3, equations (3.21), (3.23) · ASD-BOOK-ddbade997b45

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ASD-WEB-EM-022 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.

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Adopted source, conditions and previous versions

Final collected manuscript · Chapter 3, equations (3.21), (3.23)

Follows from the chosen minimal coupling; it is not used to prove the origin of the LVE magnetic correction.

Conditions retained in this adoption

  • Special two-body result: uniform exterior background, equal parallel velocities, transverse separation and virtual displacement at fixed velocity.
  • Free Maxwell representation: long waves, weak perturbations, transverse constraint, constant coefficients and normalization.
  • Minimal-coupling sources: macroscopic coarse graining, low-speed point sources or a low-frequency near zone; high-speed closed sources require separate construction.

Specific unresolved source issues

  • Local results do not automatically close high-speed topological sources, full instrument mapping or global directed propagation.

Source locators: p1002 · p1015 · p1044 · p1046 · p1048 · p1053 · p1058 · p1063 · p1067 · p1073 · p1075 · p1080 · p1085 · p1090 · p1096 · p1128 · p1153 · p1154 · p1155 · 最终合订稿 · 第三章式 (3.21)、(3.23)

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

EM-f06476f55cae · 第三章 / Chapter 3 · (3.21)–(3.23), PDF p. 7

DEPENDS ON

Dependencies

algebraMinimal coupling as an effective constitutive choiceASD-WEB-EM-021algebraPotential representation of the fieldsASD-WEB-EM-016
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