Metaphysics is a branch of philosophy that deals with deep questions of life and existence. Although the overt theme of "The Rime of the Ancient Mariner" is that a person should love all the creatures God has created, one can nevertheless identify various metaphysical themes that the poem grapples with as well. The most obvious metaphysical topics of the poem are determinism and free will, mind and matter, and religion and spirituality.
Determinism is the concept that everything that happens is destined to happen based on events that have already ocurred. Determinism stands opposed to free will, which states that people can determine their own actions and outcomes. In "Rime," the mariner shoots the albatross for no apparent reason, and this sets in motion a series of dire consequences for him and others. A deterministic perspective would see that the mariner had no choice but to shoot the albatross; all the events of his life up to that point brought him to the place where that was what he was going to do in that situation. Interestingly, his redemption comes through no choice of his own: he looks at the water snakes and "blessed them unaware." Later, he spends his life going into an unavoidable spasm when he finds the person he must tell his tale to. He really has no free will even after he returns home.
In the poem, both mind and matter affect the mariner. He deals with significant physical problems including ice, lack of wind, desperate thirst, and a sinking boat. The mariner's mind is incapable of solving these problems; however, his mental torment does make his problems worse. He considers the curse in the dead men's eyes, he experiences friendship and fear, and he wonders at all the things happening to him. So the poem seems to suggest that both mind and matter are real and contribute to one's experience.
Religion and spirituality play a big part in the poem. Some Christian orthodoxy is displayed as references are made to the Virgin Mary and to Christ and to the hermit's ability to "shrieve" the mariner. However, the poem contains more references to the "polar spirits" that decree that the mariner must "do penance." Each "seraph-man" that occupies a dead man's corpse is another example of the spirit world presented by this poem. The mariner's ability to pray is what turns his fortune and allows his redemption. Coleridge creates a mythical spirit world that he blends with elements of Christianity and in so doing validates the idea of an unseen spiritual dimension.
Certainly some metaphysical themes are present in "The Rime of the Ancient Mariner," although they are not Coleridge's primary emphasis. Nevertheless, themes of determinism, mind and matter, and religion and spirituality are evident in the poem.