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---
## 当前已知
运动伴随场的源方程已经有明确的构造起点：把静态核心及其周围场平移到中心位置 $X(t)$，代入原二阶场方程，速度平方项与加速度项形成失配源。第五章式（5.1.18）—（5.1.21）给出了这一步的一阶线性化及平移零模的动能加权正交条件；投影权重来自同一作用量，用于区分核心运动和核外扰动。
式（5.1.23）—（5.1.29）进一步给出初始齐次场加推迟源积分、有限核多极展开和辐射谱交条件。式（5.2.1）—（5.2.6）已计算二维常系数通道的外向 Hankel 响应及亚阈值衰减响应，包括坐标变换的源归一化。它们说明给定源怎样激发延展或束缚伴随场。完整静态核心、有限源轮廓及其在各通道上的数值投影，则是继续把这一构造落实到具体物质的任务。
## 数学与物理任务
先从同一作用量求一个满足边界与有限能量条件的核心，计算能量二阶变分、动能内积和扰动谱；周期核心应改用周期背景与 Floquet 分析。随后把平移、内部相位、取向和速度形变分开，计算各源的实际投影、多极矩与形状因子，不能预先假定每个通道都具有非零单极矩。
用明确的初始场、源历史及外向或衰减边界求运动着装态，并检查核心反作用与远区能流。辐射条件同时需要谱交点和非零源投影；对各向同性有隙支，$\omega_s<\omega_0/\gamma$ 无交点，等号是谱相切的临界情形，不能仅由“$\leq$”推出严格低于阈值。临界源投影、通量极限及有限核正则化应单独计算。
## 可交付成果
第一份可复核成果可以限定为一个已指定作用量中的核心构型及单通道投影：提交方程、参数与单位、边界和初值、源轮廓文件、零模检查、谱、数值收敛与残差。继而给出对应共动解和能流，核对总能量中核心、伴随场及相互作用贡献是否重复计数。用解析二维响应作受控对照，明确哪些输入来自核心计算，哪些仍是规定参数。
## 不能当作完成的捷径
指定点源或写出 Hankel 函数是有效模型的已得解，不等于已经求出产生该源的完整物质结构。无净远区辐射也不自动等于无限空间总能量有限。任务的推进是把已有源方程和响应与实际核心连接起来，而不是再次声称伴随场尚无方程。
## 研究依赖
- [物质稳定性与核心构型](/theory/matter/stability)
- [伴随场的源、投影与响应](/theory/quantum/accompanying-field)
[量子现象总览](/theory/quantum) · [现象学要求](/tests/quantum)