In chapter 6 of his later discursive book "Summa Technologiae", first published in 1964, he discussed in detail the identity paradoxes associated with teleportation and hibernation of human beings.
On Mars, another machine re-creates the person (from local stores of carbon, hydrogen, and so on), each atom in exactly the same relative position.
Parfit poses the question of whether or not the teletransporter is actually a method of travel, or if it simply kills and makes an exact replica of the user.
Using thought experiments such as these, Parfit argues that any criteria we attempt to use to determine sameness of person will be lacking, because there is no further fact.
Parfit resolves the logic to reach this conclusion, which appears to justify incursion into personal freedoms, but he does not explicitly endorse such invasive control.