The Regents of the University of California are authorized and empowered to appoint one or more persons to be members of the University of California police department as such police department is constituted on September 19, 1947, or may thereafter be constituted. Persons employed and compensated as members of said police department, when so appointed and duly sworn, are peace officers; provided, that such officers shall not exercise their powers or authority except (a) upon the campuses of the University of California and an area within one mile of the exterior boundaries of each thereof, (b) in or about other grounds or properties owned, operated, controlled or administered by the Regents of the University of California, and (c) as provided in Section 830.2 of the Penal Code.