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Manuscript local dual-field functional

An explicit local dual-field action; Θ has real components and W subtracts vacuum energy. Specify stabilizers, constitutive parameters and target space; complete microscopic unification still needs joint solution.

Theory · CANDIDATE MODELEquation version 1.0.0

Based on the final manuscript · Chapters 4 and 5

ASD-WEB-SD-023
LuΘ=12Zu∣∂tu∣2+12IΘ∑A(∂tΘA)2−E0+Jext⋅u,E0=12Ku(s2+∣w∣2)+12AΘ∑A∣∇ΘA∣2+W(Θ)+gLsF(Θ)+gTw⋅T+Estab+Enl,F=∑AΘA2−v02,s=∇⋅u,w=∇×u,Ku=Zucu2.\begin{aligned}\mathcal L_{u\Theta}&=\tfrac12Z_u|\partial_t\mathbf u|^2+\tfrac12I_\Theta\sum_A(\partial_t\Theta_A)^2-\mathcal E_0+\mathbf J_{\rm ext}\cdot\mathbf u,\\\mathcal E_0&=\tfrac12K_u(s^2+|\mathbf w|^2)+\tfrac12A_\Theta\sum_A|\nabla\Theta_A|^2+W(\Theta)\\&\quad+g_LsF(\Theta)+g_T\mathbf w\cdot\mathbf T+\mathcal E_{\rm stab}+\mathcal E_{\rm nl},\\F&=\sum_A\Theta_A^2-v_0^2,\quad s=\nabla\cdot\mathbf u,\quad\mathbf w=\nabla\times\mathbf u,\quad K_u=Z_uc_u^2.\end{aligned}

An explicit local dual-field action; Θ has real components and W subtracts vacuum energy. Specify stabilizers, constitutive parameters and target space; complete microscopic unification still needs joint solution.
Chapter reference: Ch. 5 (5.6.3)–(5.6.5) · ASD-BOOK-ddbade997b45

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Ch. 5 (5.6.3)–(5.6.5)

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  • An explicit local dual-field action; Θ has real components and W subtracts vacuum energy. Specify stabilizers, constitutive parameters and target space; complete microscopic unification still needs joint solution.

Source locators: p2220–2227

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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SD-51779505a476 · Ch. 5 (5.6.3)–(5.6.5)

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