Both Lacan's "objet petit a" and Melanie Klein's "part object" are theoretical concepts used in psychoanalysis to describe objects that play a central role in human psychological development and experience.
In Klein's theory, "part objects" refer to objects that a child perceives as partial representations of a larger object, usually the mother or primary caregiver. For example, the breast is perceived as a part object that satisfies the child's hunger, and the mother's face is perceived as a part object that provides emotional comfort. Klein argues that the child's experience of part objects is fundamental to their development of object relations, and that this process shapes the child's relationships throughout their life.
Lacan's "objet petit a" refers to an object that is always desired but can never be fully attained. It is a constantly shifting object of desire that drives human behavior, but its true nature is always elusive. Lacan argues that this object is created through the symbolic order of language and culture and is thus specific to each individual's cultural and linguistic context.
While both concepts deal with objects that play a significant role in human psychology, Lacan's objet petit a is more abstract and conceptual than Klein's part objects, which are more concrete and specific. Additionally, while Klein's theory focuses on the child's development of object relations, Lacan's theory deals more broadly with human desire and motivation.