EQUATION REGISTRY

Squared amplitude first as field-energy weight

Quadratic field energy without external potential, averaged at leading slow-envelope order; the next order includes cross terms, not only gradients. This is not the Born rule.

Theory · EFFECTIVE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 5

ASD-WEB-QM-017
⟨EΦ⟩=ZΦ4[∣∂tΨ−iω0Ψ∣2+c2Bij∂iΨ∗∂jΨ+ω02∣Ψ∣2]≃ZΦω022∣Ψ∣2\langle\mathcal E_\Phi\rangle=\frac{Z_\Phi}{4}\left[|\partial_t\Psi-i\omega_0\Psi|^2+c^2B_{ij}\partial_i\Psi^*\partial_j\Psi+\omega_0^2|\Psi|^2\right]\simeq\frac{Z_\Phi\omega_0^2}{2}|\Psi|^2

Quadratic field energy without external potential, averaged at leading slow-envelope order; the next order includes cross terms, not only gradients. This is not the Born rule.
Chapter reference: Ch. 5 (5.1.36) · ASD-BOOK-ddbade997b45

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Ch. 5 (5.1.36)

Quadratic field energy without external potential, averaged at leading slow-envelope order; the next order includes cross terms, not only gradients. This is not the Born rule.

Conditions retained in this adoption

  • Selected channel and stated initial/boundary conditions; action/energy matching retained
  • Continuum, slow-envelope and detector approximations kept at their respective levels

Source locators: p1770 · p1803 · p1826 · p1833 · p1837 · p1841

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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QM-0accdcbe7725 · Ch. 5 (5.1.36)

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