摘要： Symmetry-based analysis is very useful in many fields of science. In the case of time-dependent systems, the symmetries of interest are dynamical, and are maintained during the system’s evolution in time. Interestingly, such symmetries may manifest over several length scales, e.g. both microscopically and macroscopically. For example, in high harmonic generation (HHG), micro-scale dynamical symmetries (DSs) yield selection rules that forbid some harmonic orders and determine the polarizations of the allowed harmonics [1], as was formulated recently in a consistent group theory [2]. Macroscopically, DSs of the wave equation may induce selection rules with respect to phase-matching conditions and conservation of angular or linear momentum [3]. However, the DSs of these different length scales are generally thought to be non-interacting, and have so far only been described separately. Here we formulate and explore plethora of multi-scale dynamical symmetries (MSDS), where the symmetry operations involve both microscopic and macroscopic length scales. We derive all possible MSDS operations and their resulting selection rules in HHG, and experimentally demonstrate non-trivial selection rules of the new theory.