拓扑介导的引力：宇宙学常数问题的分类解决
Topos Mediated Gravity: Toward the Categorical Resolution of the Cosmological Constant Problem
摘要：
根据Döring和Isham，光谱拓扑对应于任何量子系统。在拓扑中对系统的描述变得类似于经典理论所给出的描述，直到观测量的倍增。突现理论的逻辑是直觉主义的，而不是经典的。在语言中添加自伴算子及其积的类型，这些算子及其积由舞台上的daseinisation及其积解释，人们在topos中获得了通勤预层。的解释同意舞台上daseinisations广场的一些自同构的拓扑结构。不确定原理不适用于这种解释。根据作者最近提出的观点，拓扑可以改变局部光滑时空结构。提出了一种在系统的光谱拓扑图中加入重力的方法。假设一个量子系统改变了局域时空结构，并通过谱拓扑与引力场相互作用，则量子谐振子的最低能量模将被引力抵消。此外，引力和系统的理论应该关于拓扑范畴的2-群自同构对称。在量子谐振子哈密顿量的$δ_0$解释下，它的最低模对宇宙学常数的贡献为零。这与引力的基本更高对称群有关。没有$δ_0$解释，有效宇宙学常数的小的非零值可以接近。
英文摘要：
According to Döring and Isham the spectral topos corresponds to any quantum system. The description of a system in the topos becomes similar to this given by classical theory, up to multiplication of observables. Logic of the emergent theory is rather intuitionistic than classical. Adding to the language the type of self-adjoint operators and their products, which are interpreted by the on-stages daseinisations and their products, one gets commuting presheaves in the topos. The interpretation agrees with on-stages daseinisations of squares up to some automorphisms of the topos. The uncertainty principle does not hold for such an interpretation. According to the recent proposition by the author, topoi can modify local smooth spacetime structure. A way how to add gravity into the spectral topos of a system is presented. Assuming that a quantum system modifies the local spacetime structure and interacts with a gravitational field via the spectral topos, the lowest energy modes of a quantum harmonic oscillator are gravitationally nullified. Moreover, a theory of gravity and systems should be symmetric with respect to the 2-group of automorphisms of the category of topoi. Under the $δ_0$-interpretation for the hamiltonian of a quantum harmonic oscillator, its lowest modes have vanishing contributions to the cosmological constant. This is related with a fundamental higher symmetry group of gravity. Without the $δ_0$-interpretation, small non-zero value of the effective cosmological constant can be approached.
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