确定性固有时框架中玻色与费米代数的普适涌现

中文摘要 AI 辅助

本工作发展了我们此前工作（Eur. Phys. J. C \textbf{86} (2026) 829）中提出的确定性离散固有时框架，在该框架中量子场论作为有效红外描述涌现，其特征是跑动的普朗克常数。此前，有效量子化标度由粗粒化无法分辨的微观多重性推断得出；此处我们提供其动力学与算符实现，并将该构造扩展至费米自由度。首先，宏观分辨率变化下的自洽性导出了重整化群方程的结构，而跑动普朗克常数支配着向确定性 regime 的过渡。其次，我们通过场构型空间中的有限差分平移来表示可逆微观动力学，粗粒化后，所得算符值正则对易关系重现了此前从统计微观态计数得到的同一量子化标度，从而将微观演化与涌现的正则代数关联起来。第三，在格拉斯曼代数中表示同一更新，得到了对应的正则反对易关系。因此，玻色与费米 sector 继承了共同的有效普朗克常数，无需引入独立的费米更新或量子化标度。最后，我们讨论了其对高能圈振幅与有效霍金辐射的可能启示。

英文摘要

This work develops the deterministic, discrete proper-time framework introduced in our previous work, Eur.\ Phys.\ J.\ C \textbf{86} (2026) 829, in which quantum field theory emerges as an effective infrared description characterized by a running Planck constant. There, the effective quantization scale was inferred from the microscopic multiplicity unresolved by coarse-graining. Here, we provide its dynamical and operatorial realization and extend the construction to fermionic degrees of freedom. First, consistency under changes of macroscopic resolution leads to the structure of the Renormalization Group Equation, while the running Planck constant governs the crossover toward the deterministic regime. Second, we represent the reversible microscopic dynamics through finite-difference translations in field-configuration space. After coarse-graining, the resulting operator-valued canonical commutation relations reproduce the same quantization scale previously obtained from statistical microstate counting, thereby linking microscopic evolution to the emergent canonical algebra. Third, representing the same update within a Grassmann algebra yields the corresponding canonical anticommutation relations. The bosonic and fermionic sectors thus inherit a common effective Planck constant without introducing an independent fermionic update or quantization scale. Finally, we discuss possible implications for high-energy loop amplitudes and effective Hawking radiation.

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41 pages