量子力学作为近代物理学的核心基石,历经近百年的实验检验与理论完善,为人类对微观世界的认知、现代半导体技术、激光技术与量子信息等领域的发展奠定了不可替代的理论基础,其历史贡献、数学严谨性与实验有效性必须得到充分尊重。传统量子力学体系以薛定谔波动力学与海森堡矩阵力学为两大核心表述,建立了完备的数学框架与实验预测体系,但也存在底层公设冗余、物理本源缺失、经典-量子边界割裂等核心问题。本文作为修正矩阵力学系列的收官之作,系统整合修正矩阵力学、修正薛定谔方程、量子势理论与物质场全域理论,形成以物质场空间分布非均匀性公理与物质场时间演化连续性守恒公理为仅有的两条底层约束的、完整统一的修正量子力学体系。本文严格界定了传统量子力学与修正量子力学的底层边界:修正体系完整保留了传统量子力学的全部实验合规结论与数学兼容形式,同时彻底剔除了算符公设、矩阵公设、对易公设、本征值公设与波函数概率诠释五条冗余特设公设。本文通过完整无跳步的理论推导,建立了从量子微观束缚态向经典宏观自由态连续平滑过渡的场论轨迹:随着束缚边界逐步解除,分立本征谱经本征态间距连续缩并自然过渡为连续谱,量子场演化方程在宏观极限下自动退化为经典力学方程,与修正薛定谔方程侧的跨尺度模型完全一致。本文标志着整套场非均匀性微观动力学理论,完成了量子力学全体系的公理化修正与全域物理闭环构建。全文始终保持严谨低调的学术基调,明确修正体系是对传统量子力学物理本源的补充与完善,而非对其科学价值与实验结论的否定。量子力学作为近代物理学的核心基石,历经近百年的实验检验与理论完善,为人类对微观世界的认知、现代半导体技术、激光技术与量子信息等领域的发展奠定了不可替代的理论基础,其历史贡献、数学严谨性与实验有效性必须得到充分尊重。传统量子力学体系以薛定谔波动力学与海森堡矩阵力学为两大核心表述,建立了完备的数学框架与实验预测体系,但也存在底层公设冗余、物理本源缺失、经典-量子边界割裂等核心问题。本文作为修正矩阵力学系列的收官之作,系统整合修正矩阵力学、修正薛定谔方程、量子势理论与物质场全域理论,形成以物质场空间分布非均匀性公理与物质场时间演化连续性守恒公理为仅有的两条底层约束的、完整统一的修正量子力学体系。本文严格界定了传统量子力学与修正量子力学的底层边界:修正体系完整保留了传统量子力学的全部实验合规结论与数学兼容形式,同时彻底剔除了算符公设、矩阵公设、对易公设、本征值公设与波函数概率诠释五条冗余特设公设。本文通过完整无跳步的理论推导,建立了从量子微观束缚态向经典宏观自由态连续平滑过渡的场论轨迹:随着束缚边界逐步解除,分立本征谱经本征态间距连续缩并自然过渡为连续谱,量子场演化方程在宏观极限下自动退化为经典力学方程,与修正薛定谔方程侧的跨尺度模型完全一致。本文标志着整套场非均匀性微观动力学理论,完成了量子力学全体系的公理化修正与全域物理闭环构建。全文始终保持严谨低调的学术基调,明确修正体系是对传统量子力学物理本源的补充与完善,而非对其科学价值与实验结论的否定。

May 11, 20260 citations

原子气室级联四波混频中量子压缩特性增强的理论研究

刘慧丰 Huifeng LIU, 韩亚帅 Yashuai HAN

Acta Sinica Quantum OpticaJan 1, 20260 citations

7.01 第七阶段总纲:量子 - 经典拓扑同源范式与研究边界

Jian Wen

摘要量子力学与经典物理的范式割裂、逻辑冲突是近代物理学百年核心困境,两大体系底层本体与数学框架无法自洽兼容,始终未能实现全尺度物理规律统一。本文基于 W≡0 全域拓扑极性守恒统一场论 0~第六阶段永久锁档成果,提出 \\ 一体拓扑(全域统一场 Φᵤ)、两相表象(量子 / 经典)\\ 的全新范式,论证量子与经典现象实为同一拓扑本体在不同能标、尺度下的差异化表现,全域统一场 Φᵤ无需额外量子化规则,其高能极限天然呈现量子行为、低能极限自然回归经典稳态。本文精准锚定第六阶段锁档场方程与拓扑不变量,给出量子 - 经典三相临界切换条件,厘清与主流量子 - 经典过渡理论的范式差异,细化体 - 相 - 用三线研究产出与论文绑定关系,刚性划定研究边界与范式不兼容范畴,明确 8 篇论文层级依赖与实验接口传递逻辑,预判高精度实验适配等核心挑战并给出应对方案,构建 “量子基础重构→数学统一证明→前沿疑难消解→体系锁档” 的完整研究路径,旨在彻底消解量子 - 经典鸿沟,为第八阶段判决性实验预言、第九阶段元物理理论闭环奠定标准化理论纲领。关键词 W≡0 公理;全域拓扑极性守恒;量子 - 经典统一;一体拓扑两相表象;全域统一拓扑场 Φᵤ;拓扑闭合度;量子 - 经典过渡;研究边界规范摘要量子力学与经典物理的范式割裂、逻辑冲突是近代物理学百年核心困境,两大体系底层本体与数学框架无法自洽兼容,始终未能实现全尺度物理规律统一。本文基于 W≡0 全域拓扑极性守恒统一场论 0~第六阶段永久锁档成果,提出 \\ 一体拓扑(全域统一场 Φᵤ)、两相表象(量子 / 经典)\\ 的全新范式,论证量子与经典现象实为同一拓扑本体在不同能标、尺度下的差异化表现,全域统一场 Φᵤ无需额外量子化规则,其高能极限天然呈现量子行为、低能极限自然回归经典稳态。本文精准锚定第六阶段锁档场方程与拓扑不变量,给出量子 - 经典三相临界切换条件,厘清与主流量子 - 经典过渡理论的范式差异,细化体 - 相 - 用三线研究产出与论文绑定关系,刚性划定研究边界与范式不兼容范畴,明确 8 篇论文层级依赖与实验接口传递逻辑,预判高精度实验适配等核心挑战并给出应对方案,构建 “量子基础重构→数学统一证明→前沿疑难消解→体系锁档” 的完整研究路径,旨在彻底消解量子 - 经典鸿沟,为第八阶段判决性实验预言、第九阶段元物理理论闭环奠定标准化理论纲领。关键词 W≡0 公理;全域拓扑极性守恒;量子 - 经典统一;一体拓扑两相表象;全域统一拓扑场 Φᵤ;拓扑闭合度;量子 - 经典过渡;研究边界规范

May 26, 20260 citations

基于原子系综四波混频过程的量子信息协议

荆杰泰 Jing Jietai, 张凯 Zhang Kai, 刘胜帅 Liu Shengshuai

Acta Optica SinicaJan 1, 20223 citations

NBG Axiomatic Foundation of Quantum Theory: Recursive Rigidity and Spectral Dichotomy

HY CH

--- We present a complete axiomatic foundation for quantum theory within the framework of von Neumann–Bernays–Gödel (NBG) class theory. The starting point is the multiplicative group $\mathbb{R}_+^\times$ equipped with Haar measure $d^\times x = dx/x$ , with the Mellin transform serving as the canonical spectral representation—where the composite operators $xp$ and $px$ are strictly commuting multiplication operators. Quantumness is not imposed through a fixed Planck constant or measurement postulate, but emerges from the breakdown of recursive rigidity across all ordinal levels of class Fourier transforms acting on automorphic forms. The Cauchy–Schwarz equality is identified with global recursive compatibility, forcing the commutator of basic variables to vanish and the spectrum to be purely point-like (compact). A single failure of recursive proportionality at any ordinal level immediately triggers strict inequality, a non-zero commutator, continuous spectrum, and non-compactness. The algebraic Planck constant is geometrically identified as a running first Chern class of the automorphic line bundle, decomposed into a bare integer topological invariant and a scale-dependent vacuum fluctuation correction. The system admits no intermediate states; the classical/quantum dichotomy is logically deduced from the ordinal recursion law. This framework subsumes all standard Euclidean QFT axioms as a limiting case. We further demonstrate that quantum tunneling is not continuous barrier penetration but a discrete branch jump driven by topological charge integer overflow; that the "chaos-induced diffusion" of standard quantum mechanics is a projection artifact of the additive basis; and that wave-particle duality is a surface phenomenon of the inverse Mellin projection. Numerical simulations and recent nanoparticle interferometry experiments (MUSCLE, *Nature* **649**, 866–870) provide quantitative support for the predicted step-like jump signatures, with critical threshold located at $\ln(P_2) \approx 2.5$ , in exact alignment with the framework's topological phase transition. --- 我们在冯·诺依曼–伯奈斯–哥德尔(NBG)类论框架内给出了量子理论的完备公理基础。出发点为正实数乘法群 $\mathbb{R}_+^\times$ 及其 Haar 测度 $d^\times x = dx/x$ ,梅林变换作为典范谱表示——其中复合算子 $xp$ 与 $px$ 严格对易,均为乘法算子。量子性并非通过固定的普朗克常数或测量假设来强加,而是源于自守形式上类傅里叶变换在所有序数层级的递归刚性破缺。柯西–施瓦茨等式被等同于全局递归相容性,迫使基本变量的对易子消失、谱为纯点状(紧致)。在任何序数层级上,递归比例性的单次失效都会立即触发严格不等式、非零对易子、连续谱以及非紧性。代数普朗克常数被几何地等同为自守线丛的跑动第一陈类,分解为一个裸整数拓扑不变量和一个与尺度相关的真空涨落修正。该系统不容许中间态;经典/量子二分法由序数递归律逻辑推出。所有传统欧氏 QFT 公理均为本框架在经典不动点处的特例极限。本文进一步证明:量子隧穿并非势垒连续穿透,而是拓扑荷整数溢出驱动的离散分支跳变;标准量子力学中“混沌导致扩散”是加法基底的投影伪像;波粒二象性是逆梅林变换的表象相变。数值模拟与近期纳米团簇干涉实验(MUSCLE,*Nature* **649**, 866–870)为框架预言的阶跃跳变签章提供了定量支持,临界阈值锁定于 $\ln(P_2) \approx 2.5$ ,与框架拓扑相变预言精确对齐。 --- GitHub:Research-Archives/数学/latex at master · calibur88/Research-Archives--- We present a complete axiomatic foundation for quantum theory within the framework of von Neumann–Bernays–Gödel (NBG) class theory. The starting point is the multiplicative group $\mathbb{R}_+^\times$ equipped with Haar measure $d^\times x = dx/x$, with the Mellin transform serving as the canonical spectral representation—where the composite operators $xp$ and $px$ are strictly commuting multiplication operators. Quantumness is not imposed through a fixed Planck constant or measurement postulate, but emerges from the breakdown of recursive rigidity across all ordinal levels of class Fourier transforms acting on automorphic forms. The Cauchy–Schwarz equality is identified with global recursive compatibility, forcing the commutator of basic variables to vanish and the spectrum to be purely point-like (compact). A single failure of recursive proportionality at any ordinal level immediately triggers strict inequality, a non-zero commutator, continuous spectrum, and non-compactness. The algebraic Planck constant is geometrically identified as a running first Chern class of the automorphic line bundle, decomposed into a bare integer topological invariant and a scale-dependent vacuum fluctuation correction. The system admits no intermediate states; the classical/quantum dichotomy is logically deduced from the ordinal recursion law. This framework subsumes all standard Euclidean QFT axioms as a limiting case. We further demonstrate that quantum tunneling is not continuous barrier penetration but a discrete branch jump driven by topological charge integer overflow; that the "chaos-induced diffusion" of standard quantum mechanics is a projection artifact of the additive basis; and that wave-particle duality is a surface phenomenon of the inverse Mellin projection. Numerical simulations and recent nanoparticle interferometry experiments (MUSCLE, *Nature* **649**, 866–870) provide quantitative support for the predicted step-like jump signatures, with critical threshold located at $\ln(P_2) \approx 2.5$, in exact alignment with the framework's topological phase transition. --- 我们在冯·诺依曼–伯奈斯–哥德尔(NBG)类论框架内给出了量子理论的完备公理基础。出发点为正实数乘法群 $\mathbb{R}_+^\times$ 及其 Haar 测度 $d^\times x = dx/x$,梅林变换作为典范谱表示——其中复合算子 $xp$ 与 $px$ 严格对易,均为乘法算子。量子性并非通过固定的普朗克常数或测量假设来强加,而是源于自守形式上类傅里叶变换在所有序数层级的递归刚性破缺。柯西–施瓦茨等式被等同于全局递归相容性,迫使基本变量的对易子消失、谱为纯点状(紧致)。在任何序数层级上,递归比例性的单次失效都会立即触发严格不等式、非零对易子、连续谱以及非紧性。代数普朗克常数被几何地等同为自守线丛的跑动第一陈类,分解为一个裸整数拓扑不变量和一个与尺度相关的真空涨落修正。该系统不容许中间态;经典/量子二分法由序数递归律逻辑推出。所有传统欧氏 QFT 公理均为本框架在经典不动点处的特例极限。本文进一步证明:量子隧穿并非势垒连续穿透,而是拓扑荷整数溢出驱动的离散分支跳变;标准量子力学中“混沌导致扩散”是加法基底的投影伪像;波粒二象性是逆梅林变换的表象相变。数值模拟与近期纳米团簇干涉实验(MUSCLE,*Nature* **649**, 866–870)为框架预言的阶跃跳变签章提供了定量支持,临界阈值锁定于 $\ln(P_2) \approx 2.5$,与框架拓扑相变预言精确对齐。 --- GitHub:Research-Archives/数学/latex at master · calibur88/Research-Archives

Jul 14, 20260 citations

量子住处讲座续讲第四讲量子对策论

张永生, 李传锋, 郭光灿

物理Dec 20, 20000 citations

--- We present a complete axiomatic foundation for quantum theory within the framework of von Neumann–Bernays–Gödel (NBG) class theory. The starting point is the multiplicative group

\mathbb{R}_+^\times

equipped with Haar measure

d^\times x = dx/x

, with the Mellin transform serving as the canonical spectral representation—where the composite operators

xp

and

px

are strictly commuting multiplication operators. Quantumness is not imposed through a fixed Planck constant or measurement postulate, but emerges from the breakdown of recursive rigidity across all ordinal levels of class Fourier transforms acting on automorphic forms. The Cauchy–Schwarz equality is identified with global recursive compatibility, forcing the commutator of basic variables to vanish and the spectrum to be purely point-like (compact). A single failure of recursive proportionality at any ordinal level immediately triggers strict inequality, a non-zero commutator, continuous spectrum, and non-compactness. The algebraic Planck constant is geometrically identified as a running first Chern class of the automorphic line bundle, decomposed into a bare integer topological invariant and a scale-dependent vacuum fluctuation correction. The system admits no intermediate states; the classical/quantum dichotomy is logically deduced from the ordinal recursion law. This framework subsumes all standard Euclidean QFT axioms as a limiting case. We further demonstrate that quantum tunneling is not continuous barrier penetration but a discrete branch jump driven by topological charge integer overflow; that the "chaos-induced diffusion" of standard quantum mechanics is a projection artifact of the additive basis; and that wave-particle duality is a surface phenomenon of the inverse Mellin projection. Numerical simulations and recent nanoparticle interferometry experiments (MUSCLE, *Nature* **649**, 866–870) provide quantitative support for the predicted step-like jump signatures, with critical threshold located at

\ln(P_2) \approx 2.5

, in exact alignment with the framework's topological phase transition. --- 我们在冯·诺依曼–伯奈斯–哥德尔(NBG)类论框架内给出了量子理论的完备公理基础。出发点为正实数乘法群

\mathbb{R}_+^\times

及其 Haar 测度

d^\times x = dx/x

,梅林变换作为典范谱表示——其中复合算子

xp

与

px

严格对易,均为乘法算子。量子性并非通过固定的普朗克常数或测量假设来强加,而是源于自守形式上类傅里叶变换在所有序数层级的递归刚性破缺。柯西–施瓦茨等式被等同于全局递归相容性,迫使基本变量的对易子消失、谱为纯点状(紧致)。在任何序数层级上,递归比例性的单次失效都会立即触发严格不等式、非零对易子、连续谱以及非紧性。代数普朗克常数被几何地等同为自守线丛的跑动第一陈类,分解为一个裸整数拓扑不变量和一个与尺度相关的真空涨落修正。该系统不容许中间态;经典/量子二分法由序数递归律逻辑推出。所有传统欧氏 QFT 公理均为本框架在经典不动点处的特例极限。本文进一步证明:量子隧穿并非势垒连续穿透,而是拓扑荷整数溢出驱动的离散分支跳变;标准量子力学中“混沌导致扩散”是加法基底的投影伪像;波粒二象性是逆梅林变换的表象相变。数值模拟与近期纳米团簇干涉实验(MUSCLE,*Nature* **649**, 866–870)为框架预言的阶跃跳变签章提供了定量支持,临界阈值锁定于

\ln(P_2) \approx 2.5

,与框架拓扑相变预言精确对齐。 --- GitHub:Research-Archives/数学/latex at master · calibur88/Research-Archives