有限分辨率对量子唯一性的限制
Finite-Resolution Limits on Quantum Uniqueness
浏览论文内容
中文总结 AI 辅助
该研究指出有限分辨率无法验证魏尔平移群的强连续性假设，正则魏尔表示与非正则聚合物表示在有限协议下的期望值可任意接近，需额外输入区分两者。
中文摘要 AI 辅助
斯通-冯·诺依曼定理仅在对魏尔平移群施加强连续性条件后，才使正则量子化具有唯一性。我们证明，这种连续性假设无法通过对魏尔关系的任何有限分辨率质询来验证。有限协议仅探测有限多个相空间位移和有界期望值，从而确定由魏尔平移的有限生成子群生成的协议代数\ntitle_cn有限分辨率对量子唯一性的限制
英文摘要
The Stone-von Neumann theorem makes canonical quantization unique only after one imposes strong continuity of the Weyl translation groups. We show that this continuity assumption cannot be certified by any finite-resolution interrogation of the Weyl relations. A finite protocol probes only finitely many phase-space displacements and bounded expectation values, thereby determining a protocol algebra \(C_S\) generated by a finitely generated subgroup of Weyl translations, but not the regularity of an extension to the full Weyl algebra. Using the polymer representation as a canonical non-regular representation, we prove that for every regular Weyl representation, every normal state, and every finite family of bounded protocol observables, a polymer state reproduces the same expectation values to arbitrary prescribed accuracy. Thus finite agreement with Schrödinger quantum mechanics does not operationally certify the regularity hypothesis entering uniqueness. The result does not assert physical equivalence between regular and polymer quantizations, it identifies where additional input, such as Hamiltonian dynamics, energy regularity, semiclassicality, or a continuum limit, is required to distinguish or select representations. In this precise sense, non-regular polymer kinematics are not excluded by finite Weyl data alone, a point of direct relevance to quantum-gravity motivated quantizations.
