Luke 24:12

For he alone believed the women saying that they had seen Angels; and as he was of more ardent feelings than the rest, he anxiously put himself foremost, looking every where for the Lord; as it follows, And stooping down, he beheld the linen clothes laid by themselves.

If he left his clothes behind in the tomb, it was so that Adam could enter into paradise without clothing, just as he had been before he had sinned. In place of having to leave paradise clothed, he now had to strip himself before entering there [again]. Or [alternatively], he abandoned them to symbolize the mystery of the resurrection of the dead, for just as [the Lord] rose into glory without clothes, so we also [will rise] with our works and not with our clothes.

Luke is supposed to have mentioned this concerning Peter, recapitulating. For Peter ran to the sepulchre at the same time that John also went, as soon as it had been told to them alone by the women, (especially Mary Magdalene,) that the body was taken away. But the vision of Angels took place afterwards. Luke therefore mentioned Peter only, because to him Mary first told it. It may also strike one, that Luke says that Peter, not entering but stooping down, saw the linen clothes by themselves, and departed wondering, whereas John says, that he himself saw the linen clothes in the same position, and that he entered after Peter. We must understand then that Peter first saw them stooping down, which Luke mentions, John omits, but that he afterwards entered before John came in.