OP-QM-002 · Phase–Momentum Locking
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.
Based on the final manuscript · 第五章
NEEDS THEORY · Needs theory
Discuss this task01Established 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.
Constitutive input
The final manuscript adopts I=ℏ and total dressed-momentum matching, giving E=ℏω, P=ℏk and λ=h/P. Microscopic locking and universal normalization require a complete moving solution.
Chapter reference: Ch. 5 §2.3, text following (5.2.13) · ASD-BOOK-ddbade997b45
Mathematical result
The first set is the low-speed constant-B envelope. The full isotropic gapped branch with E=ℏω and P=ℏk gives vg=c²P/E=v. Momentum-dependent B requires its derivatives.
Chapter reference: Ch. 5 (5.2.14) · ASD-BOOK-ddbade997b45
02Research 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.
03The 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.
04Scope 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 · accompanying field · mass · matter wave · mass · quantum
On this page
Adopted source, conditions and previous versions
第五章 §1、§2.3、§6.8 式（5.2.9）—（5.2.14）、（5.6.30）
已得结果、继续研究任务与下一份交付；保留原问题 ID、优先级及状态。
Conditions retained in this adoption
- 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.
Source locators: p1870 · p1874 · p1877 · p1880 · p1884 · p2298
Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e
Download source identity manifest
The manifest identifies the source; it is not the complete manuscript. Adopting this source does not upgrade evidence or grant a new licence.
Previous source, retained as history
QM-0accdcbe7725 · Ch. 5 §§1.6, 2.1–2.5
CH5-ca737ec4e327 · 第五章-出版整理稿.docxca737ec4e327d72c5507bbc8e00295b6e56029c7583ebad8e505cdb9c68c6262
Position within the framework
These links index inputs and research relationships. The completion status of each derivation is specified in its text. Untranslated supporting pages open in Chinese.
Revision history
第五章 · 第五章 §1、§2.3、§6.8 式（5.2.9）—（5.2.14）、（5.6.30）
This research task is based on the cited final Chinese manuscript. It is not a new canonical result. Both languages use the same source snapshot; original equation numbers and website IDs remain distinct.
Knowledge scopeASD: OP-QM-002 · Phase–Momentum Locking. OP-QM-002-EN. Version 1.0.0; 2026-10-24. https://asd-physics.org/en/open-problems/quantum/phase-momentum-locking. 第五章 §1、§2.3、§6.8 式（5.2.9）—（5.2.14）、（5.6.30）. Source ASD-BOOK-ddbade997b45.
Continue with the assumptions, equations and sources.
These links carry this page and its source version into the research workspace. Each request pins its knowledge snapshot. Model availability is shown in the workspace; retrieval and private export remain available.