Answer with reference to "the Canonization" and "A Nocturnall upon S.Lucies Day".
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In The Canonization Donne talks of his passionate love so hot that it burns, I guess to death. They may destroy themselves in the act of burning with passion for one another, yet by the middle of the poem, Donne translates their love to a higher plane. First he compares himself and his beloved to the eagle and dove, a reference to the Renaissance idea in which the eagle flies in the sky above the earth while the dove transcends the skies to reach heaven. He immediately shifts to the image of the Phoenix, another death-by-fire symbol (the Phoenix is a bird that repeatedly burns in fire and comes back to life out of the ashes), suggesting that even though their flames of passion will consume them, the poet and his beloved will be reborn from the ashes of their love.
For the S.Lucies Day poem there is a profound sense of sorrow and loss of identity after the death of the beloved,
" All others, from all things, draw all that's good,
Life, soul, form, spirit, whence they being have ;
I, by Love's limbec, am the grave
Of all, that's nothing."
For Donne, death means not only the loss of the vessel (the body) but with it the loss of love,
".. often absences Withdrew our souls, and made us carcasses."
It would seem the physical body and "love" are one and the same.
That's my take!