  The study of high-speed rotating matter is a crucial research topic in
physics due to the emergence of novel phenomena. In this paper, we combined
cranking covariant density functional theory (CDFT) with a similar
renormalization group approach to decompose the Hamiltonian from the cranking
CDFT into different Hermit components, including the non-relativistic term, the
dynamical term, the spin-orbit coupling, and the Darwin term. Especially, we
obtained the rotational term, the term relating to Zeeman effect-like, and the
spin-rotation coupling due to consideration of rotation and spatial component
of vector potential. By exploring these operators, we aim to identify novel
phenomena that may occur in rotating nuclei. Signature splitting, Zeeman
effect-like, spin-rotation coupling, and spin current are among the potential
novelties that may arise in rotating nuclei. Additionally, we investigated the
observability of these phenomena and their dependence on various factors such
as nuclear deformation, rotational angular velocity, and strength of magnetic
field.
