Object a is the object that causes desire. Here, as is common in logic, a letter is used so as to avoid the confusion of meaning that could arise from the use of a more specific term.
At first, Jacques Lacan intended that a would designate the small other (autre )—that is, the fellow being—as an erotic object (Seminar 5, Formations of the Unconscious, 1957-58). Later, after having shown that lack is what makes the erotic object, Lacan used a to designate both what symbolizes this lack and also the lack itself.
In Desire and Its Interpretation, his seminar of 1958-59, Lacan used a to designate that part of the body given up in symbolic sacrifice. Its relationship of conjunction and disjunction with the barred subject is what constitutes the fantasy, as expressed in the formula, /S } a. It is disjoined from the subject, it is not the object that desire aims at, but rather it organizes the imaginary scenario of the fantasy which orders desire: a is thus the cause of desire (Seminar 10, Anxiety, 1962-63). Should object a become conjoined with the subject, this cannot be considered a recovery. It also does not imply that the subject has some knowledge of the object. It is rather the transitory abolition of subject (aphanisis) in the face of the object, where the object is not the subject's complement, but its substitute.
Lacan believed that the original subject was sustained, prior to the loss of the object and the constitution of the fantasy, by what Donald W. Winnicott described as the transitional object. And referring to a later stage in the infant's life, he saw the reel in the fort/da game as a symbol of the part of the of the body that was being detached (and not as a symbol for the mother; to Lacan, separation was not about an infant separating from a mother, but rather about each of them separating from the object a ).
Lacan differentiated four objects a, which he called "fragments of the body" (1975, p. 189): the breast, feces, the look, and the voice, each of which related to a bodily orifice and corresponded to a partial drive. These objects are not placed in developmental order. They are all designated by the same letter because they all have the same function, to symbolize castration. Object a is a partial object, but there is no corresponding whole object because a, insofar as it is lacking, creates an obstacle to any kind of totality.
The lost object could certainly be grasped in the imaginary register (as the breast from which the infant is separated or the feces that the infant rejects, for example), but that should not obscure the fact that Lacan used a to designate the real insofar is it is inexpressible by speech (thus the breast, as object a, is the inexpressible remainder of the oral demand). Object a is also outside of the phenomenal field, neither perceptible in the image of the body, nor in objects in the world.
This is why a is "the object that does not correspond to any idea," that is, "representation" (1975, p. 183). It is an object that can only be approached or delimited in logical or topological ways. Very early on, Lacan designated that which discourse made ungraspable as the "metonymic object," that is, the object that slides under the signifying chain. Later, he formalized a as the hole that hollows out the repetition of the demand (as in the model of the torus), like the disk that separates the cut from the signifier (as in the model of a cross-cap, a topological figure without edges that Lacan used to define the relations of the subject with the object as cause of desire). Then he defined a as the loss produced by the articulation of S1 and S2. This loss, which results from a subtraction of jouissance by discourse, is what Lacan called "surplus jouissance," and it is homologous with Marx's "surplus value." The equivocal nature of this term, which in French can mean both "more enjoyment" and "no more enjoyment," indicates that something of this jouissance is regained in the functioning of the drive, which "gets around" (fait le tour ) object a, in the sense that it both "circles" it and "evades" it. Starting in 1975, with the introduction of the Borromean knot, a became the point at which the three consistencies R, S, and I (Real, Symbolic, and Imaginary) are joined together, a kind of entry point for all jouissance.
Lacan considered his elaboration of object a as an extension of the discoveries of Karl Abraham and Winnicott and as opposed to object relations theory, which for him was confined to the register of the imaginary. This elaboration referred to Freud's distinction between narcissistic libido and object libido and refuses to consider the latter simply as a portion of the former that had somehow "overflowed," but instead wanted to show their structural difference. Lacan attempted to specify the mechanisms of object a 's diverse manifestations (anxiety is related to the emergence of a, and thus to the look in anxiety) and to establish clinical distinctions in relation to object a (the neurotic seeks to obtain object a by demand; the pervert makes object a the absolute condition of desire; and the psychotic keeps his objects a "in his pocket"). Lacan's work on object a has clinical implications because it directs the treatment toward a separation between the identification with the ego ideal and identification with the object a. This approach allows the analysand at the end of treatment to know the object of his or her fantasy.
See also: Demand; Deprivation; Fantasy, formula of; Fort-Da; Four discourses; Jouissance (Lacan); Knot; L and R schemas; Metonymy; Object; Other, the; Seminar, Lacan's; Sexuation, formulas of; Signifier; Signifier/signified; Signifying chain; Subject of the drive; Subject's castration; Subject's desire; Topology; Want of being/lack of being.
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