Objection 1. It would seem that Christ's was not identically the same body living and dead. For Christ truly died just as other men do. But the body of everyone else is not simply identically the same, dead and living, because there is an essential difference between them. Therefore neither is the body of Christ identically the same, dead and living.
Objection 2. Further, according to the Philosopher (Metaph. v, text. 12), things specifically diverse are also numerically diverse. But Christ's body, living and dead, was specifically diverse: because the eye or flesh of the dead is only called so equivocally, as is evident from the Philosopher (De Anima ii, text. 9; Metaph. vii). Therefore Christ's body was not simply identically the same, living and dead.
Objection 3. Further, death is a kind of corruption. But what is corrupted by substantial corruption after being corrupted, exists no longer, since corruption is change from being to non-being. Therefore, Christ's body, after it was dead, did not remain identically the same, because death is a substantial corruption.
On the contrary, Athanasius says (Epist. ad Epict.): "In that body which was circumcised and carried, which ate, and toiled, and was nailed on the tree, there was the impassible and incorporeal Word of God: the same was laid in the tomb." But Christ's living body was circumcised and nailed on the tree; and Christ's dead body was laid in the tomb. Therefore it was the same body living and dead.
I answer that, The expression "simply" can be taken in two senses. In the first instance by taking "simply" to be the same as "absolutely"; thus "that is said simply which is said without addition," as the Philosopher put it (Topic. ii): and in this way the dead and living body of Christ was simply identically the same: since a thing is said to be "simply" identically the same from the identity of the subject. But Christ's body living and dead was identical in its suppositum because alive and dead it had none other besides the Word of God, as was stated above (Article 2). And it is in this sense that Athanasius is speaking in the passage quoted.
In another way "simply" is the same as "altogether" or "totally": in which sense the body of Christ, dead and alive, was not "simply" the same identically, because it was not "totally" the same, since life is of the essence of a living body; for it is an essential and not an accidental predicate: hence it follows that a body which ceases to be living does not remain totally the same. Moreover, if it were to be said that Christ's dead body did continue "totally" the same, it would follow that it was not corrupted--I mean, by the corruption of death: which is the heresy of the Gaianites, as Isidore says (Etym. viii), and is to be found in the Decretals (xxiv, qu. iii). And Damascene says (De Fide Orth. iii) that "the term 'corruption' denotes two things: in one way it is the separation of the soul from the body and other things of the sort; in another way, the complete dissolving into elements. Consequently it is impious to say with Julian and Gaian that the Lord's body was incorruptible after the first manner of corruption before the resurrection: because Christ's body would not be consubstantial with us, nor truly dead, nor would we have been saved in very truth. But in the second way Christ's body was incorrupt."
Reply to Objection 1. The dead body of everyone else does not continue united to an abiding hypostasis, as Christ's dead body did; consequently the dead body of everyone else is not the same "simply," but only in some respect: because it is the same as to its matter, but not the same as to its form. But Christ's body remains the same simply, on account of the identity of the suppositum, as stated above.
Reply to Objection 2. Since a thing is said to be the same identically according to suppositum, but the same specifically according to form: wherever the suppositum subsists in only one nature, it follows of necessity that when the unity of species is taken away the unity of identity is also taken away. But the hypostasis of the Word of God subsists in two natures; and consequently, although in others the body does not remain the same according to the species of human nature, still it continues identically the same in Christ according to the suppositum of the Word of God.
Reply to Objection 3. Corruption and death do not belong to Christ by reason of the suppositum, from which suppositum follows the unity of identity; but by reason of the human nature, according to which is found the difference of death and of life in Christ's body.
Source: Summa Theologica (New Advent)