Personal identity is the set of necessary and sufficient conditions that make a person the same over time.
Further reading
Broome, John (1991) Utilitarian metaphysics?, in Jon Elster & John E. Roemer (eds.) Interpersonal Comparisons of Well-Being, Cambridge: Cambridge University Press, pp. 70–95.
Parfit, Derek (1984) Reasons and Persons, Oxford: Clarendon Press, part 3.
Shoemaker, David W. (2005) Personal identity and ethics, Stanford Encyclopedia of Philosophy, December 20 (updated 11 October 2019).