To provide a biblical viewpoint (if you don't want to hear it, then ignore the rest of this post), what makes "you" more than anything else is your soul (aka "spirit"), which does not die even if your body does. What tethers the soul to the body, we don't know. The physical interface linking the spirit and body is the brain, but the spiritual counterpart is not known because we cannot "see" (sense) spiritually. People think that the brain is the mind, the part of you that thinks and feels, but that is not the case. The brain itself is just a means for relaying control from your mind (which is part of your spirit) to your body. You could think of the brain as being a keyboard or a conglomeration of peripherals, to use an analogy. The keyboard is just an interface, and so is the brain (though both are important, of course, in their respective roles ). If your brain is damaged or dies, your mind is not injured and does not die, just as if you spilled soda on your keyboard (or took a hammer to it) you would not be injured or die. The link, however, would be damaged or severed. If your keyboard is broken, you are limited in input. Perhaps you wouldn't be able to use crtan lttrs, or you wouldn't be able to type at . If your brain is damaged, you can perform certain functions (to the point where you would be considered "brain dead"), or if it is completely destroyed, your body dies.
Teleportation (though I hesitate to use the word because of its technological/sci-fi connotations) is something that is recorded in the Bible. The Holy Spirit "caught away" Philip instantly to a different location. The language there seems to indicate that Philip was "translated" from one place to another (interestingly enough, though I won't go into the details here, there are references elsewhere that indicate what we would perceive as "time travel" has/is being done to the 2 people that never died: Enoch and Elijah) instantly. The deconstruction and reconstruction of molecules and atoms appears to be something that Jesus could do as well, since He passed through solid matter on 2 occasions. I don't think that in either case that the Bible as being new people afterwards. In any case, this information doubtlessly is no use to any would-be ATOT scientists, as the Bible isn't a technical manual on having supernatural powers, but I thought I would share.