There are several synonyms for the phrase "force armed with legal authority." One common term is "law enforcement," which refers to the individuals or organizations responsible for upholding the law, such as police officers or federal agents. Another synonymous phrase is "authorized personnel," which indicates that the individual or group has been granted special permission or authority to carry out a particular task or action. "Security forces" is another term that may be used to describe individuals who have been empowered to protect a particular area or group, often through the use of force or armed response. Ultimately, these synonyms all convey the idea of individuals who have been given legal jurisdiction and authorization to use force when necessary.