---
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"title": "OP-QM-002 · Phase–Momentum Locking",
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"source_reference": "第五章 §1、§2.3、§6.8 式（5.2.9）—（5.2.14）、（5.6.30）",
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"title": "各向异性空间动力学（最终合订稿）",
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"Research still required",
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"missing_result": "Compute Noether energy–momentum and cycle action on one core–bound-near-field–accompanying-field motion family. Check that phase insertion preserves the target space, distinguish structural output from empirical calibration of h, and separate full carrier energy from carrier-removed envelope energy.",
"deliverable": "Deliver independent integrals and phase mapping for a motion family, with source, surface terms, normalization and errors; test differentiation of the full dispersion for anisotropic or momentum-dependent propagation tensors.",
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---
## Established results
The final manuscript adopts single-excitation cycle-action locking to connect the complete dressed state’s energy–momentum with accompanying-field phase. Given that matching and the gapped dispersion, group velocity, energy-centre motion and mechanical momentum have explicit relations. A source already absorbed into the dressed state and effective Hamiltonian must not be counted again as an independent drive.
## Research still required
Compute Noether energy–momentum and cycle action on one core–bound-near-field–accompanying-field motion family. Check that phase insertion preserves the target space, distinguish structural output from empirical calibration of h, and separate full carrier energy from carrier-removed envelope energy.
## The next reproducible deliverable
Deliver independent integrals and phase mapping for a motion family, with source, surface terms, normalization and errors; test differentiation of the full dispersion for anisotropic or momentum-dependent propagation tensors.
## Scope and research links
Action locking is an explicit input of the current construction. Its resulting closure should not be described as wholly absent, but adopting the input does not independently compute its universal microscopic origin.
[matter wave](/en/theory/quantum/matter-wave) · [accompanying field](/en/theory/quantum/accompanying-field) · [mass](/en/theory/matter/mass) · [matter wave](/en/theory/quantum/matter-wave) · [mass](/en/theory/matter/mass) · [quantum](/en/theory/quantum)