发表机构
Universidade Federal de Ouro Preto（欧罗普雷托联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在FLRW宇宙学与Schutz流体耦合中，通过正则变换建立约化动力学与扩展约束量子化的对应，利用双侧星约束和谱映射实现物理态构造，并以平坦尘埃模型验证。
AI 中文摘要
在FLRW宇宙学与Schutz理想流体耦合的背景下，建立了约化关系动力学与扩展约束量子化之间的受控对应关系。物质扇区中的正则变换产生了一个退参数化约束，形式为$\mathcal C=p_T+H$，其中$T$充当内部时间。在扩展的Weyl-Wigner表述中，量子约束被双侧施加。其反对称部分给出了由约化哈密顿量生成的精确Moyal演化，而其对称部分则施加了一个独立的量子壳条件。对于$\hat H$的固定自伴实现，每个支持在其负谱子空间上的约化密度算符都允许一个显式的分布扩展。能量为$E$和$E'$的谱二元组被映射到支持在$p_T=-(E+E')/2$处的时钟Wigner分布，其关系相位由$E-E'$决定。该映射保持非对角相干性，满足两个星约束，并以约化Wigner态作为其$p_T$边缘分布；因此，它在可接受的正密度扇区上是单射的。一个具有$q=1/2$和Dirichlet数据的平坦尘埃模型提供了一个显式示例：其约化谱为$(-\infty,0]$，因此可接受扇区包含所有可归一化的约化态。该对应关系适用于固定的约束代表和量子实现。
英文摘要
A controlled correspondence is established between reduced relational dynamics and extended constrained quantization in an FLRW cosmology coupled to a Schutz perfect fluid. A canonical transformation in the matter sector yields a deparametrized constraint of the form $\mathcal C=p_T+H$, with $T$ serving as an internal time. In the extended Weyl--Wigner formulation, the quantum constraint is imposed bilaterally. Its antisymmetric part gives the exact Moyal evolution generated by the reduced Hamiltonian, while its symmetric part imposes an independent quantum shell condition. For a fixed self-adjoint realization of $\hat H$, every reduced density operator supported on its negative spectral subspace admits an explicit distributional extension. A spectral dyad with energies $E$ and $E'$ is mapped to a clock Wigner distribution supported at $p_T=-(E+E')/2$, with relational phase determined by $E-E'$. The map preserves off-diagonal coherences, satisfies both star constraints, and has the reduced Wigner state as its $p_T$ marginal; it is therefore injective on the admissible positive-density sector. A flat dust model with $q=1/2$ and Dirichlet data provides an explicit example: its reduced spectrum is $(-\infty,0]$, so the admissible sector contains all normalizable reduced states. The correspondence applies to a fixed constraint representative and quantum realization.
Comments25 pages, no figures
