When discussing governance and politics, various synonyms can be used instead of "state-authority" to describe the power exercised by the government in a particular region. "Government power," "state control," and "officialdom" are all viable alternatives. If one wants to convey a more specific connotation of power, "sovereignty," "domination," and "hegemony" have more authoritarian overtones. On the other hand, "administration," "bureaucracy," and "regime" imply a more organized approach to governance. In a conversational or informal setting, "the powers that be" or simply "the state" may suffice. Ultimately, the word choice will depend on the context and nuance of the conversation at hand.