what are the psychoanalytic concepts related to the movie and how was it manifested?

The versions of Joel and Clementine that Joel sees in his memory are not real, but they are interpretations or projections of the real people. Therefore, the conciliatory conversations they have over the course of the film are essentially a figment of Joel's imagination. In an interview, Michel Gondry described having conversations with his dying father in his mind, and thought it tenuously possible to have subconscious interactions with someone you know really well. Joel's mental version of Clementine is not too far off from the real Clementine, a synthesis of her mannerisms, effects, and reactions over the two years they spent together. Nevertheless, Joel's subconscious self finds an element of closure in his relationship with Clementine; and his anger dissipates, leaving him with her final message: "Meet me in Montauk." His conscious self then takes the instruction, so Joel and Clementine are able find each other again.