标题： 漩涡、拓扑和时间 显示英文标题

标题： Vortices, topology and time

摘要： 我们将物理时间与磁场涡旋的拓扑结构联系起来。 我们基于一种单模引力的表述，其中宇宙常数$\Lambda$作为与一个变量的规范对偶，该变量在壳上变为四体积时间。 如果理论被限制为拓扑轴子形式（即电场和磁场的奇宇称乘积），这样的时间变量就成为Chern-Simons密度的空间积分。 后者等于螺旋度，因此单模时间被转化为拓扑磁场涡旋的链接数乘以它们的通量。 加上{\it 公设}表示该通量是一个普遍常数，因此时间的流动可以解释为磁场所涡旋之间逐步编织更多链接的过程，每个链接提供一个与固定通量相关的量子时间。 对非阿贝尔扩展以及目标参数不同于$\Lambda$的情况进行了简要考察，揭示了不同类型的涡旋以及链接之间的可能作用，从而导致新的现象学。 显示英文摘要

摘要： We relate physical time with the topology of magnetic field vortices. We base ourselves on a formulation of unimodular gravity where the cosmological constant $\Lambda$ appears as the canonical dual to a variable which on-shell becomes four-volume time. If the theory is restricted to a topological axionic form (viz. a parity-odd product of an electric and a magnetic field), such a time variable becomes the spatial integral of the Chern-Simons density. The latter equates to helicity, so that unimodular time is transmuted into the linking number of the vortices of the topological magnetic field, times their flux. With the added {\it postulate} that this flux is a universal constant, the flow of time can thus be interpreted as the progressive weaving of further links between magnetic field vortices, each link providing a quantum of time with value related to the fixed flux. Non-abelian extensions, and targetting parameters other than $\Lambda$ are briefly examined, exposing different types of vortices and a possible role for inter-linking leading to new phenomenology.