"How is a Greek chorus like a lawyer?" ask the chorus in Anne Carson's latest work, a translation of Sophocles' Antigone. "They're both in the business of searching for a precedent  so as to be able to say / this terrible thing we're witnessing now is / not unique you know it happened before / or something much like it." Such light-handed scholarship is characteristic of Carson, a poet interested in those moments when precedents can't be found and normal translations fail: "Now I could dig up those case histories, tell you about Danaos and Lykourgus and the songs of Phineas," they continue: "it wouldn't help you / it didn't help me / it's Friday afternoon / there goes Antigone to be buried alive."

Carson, a poet influenced by authors as diverse as Sappho, Euripides, Emily Brontë, Gertrude Stein and Virginia Woolf, is known both for innovative translations of ancient texts and for her restrained but searing confessional poetry (try "The Glass Essay" or The Beauty of the Husband). Some of her best works merge her two roles: Nox, a facsimile of Carson's own scrapbook, presented the reader with notes for a translation of a Catullus' elegy for his brother, poem 101, alongside photographs and notes detailing the history of her own brother, Michael, who died after a long disappearance. Being scholarly and methodical, Nox suggests, has its limits: "Prowling the meanings of a word, prowling the history of a person, no use expecting a flood of light," she writes. "Human beings have no main switch."

For readers of Nox, in which Carson describes poem 101 as "a room I can never leave", there is something quietly horrific about Carson's choice of Antigone for a sequel  another difficult text about mourning a brother, in which the heroine is condemned to a living death in a sealed cave. The title is disconcerting, too. That "nick" is suggestive of a chipped ancient sculpture, a prison, a critical moment  or, as Carson's cast-list suggests, a ghostly presence: Nick is "a mute part [always onstage, he measures things]."

Antigonick, a "comic book" of Sophocles' tragedy, is one of Carson's strangest works. It dramatises its own eccentricity, evoking a portrait of the author in a state of distraction; the words of the translation are printed in handwriting (Carson's own), almost entirely without punctuation, in tiny capital letters that are both neat and a little frantic. The illustrations (by the artist Bianca Stone) are a surreal assortment of icy landscapes, domestic interiors, gothic houses, unravelling spools of thread, precarious staircases and drowning horses, which are printed on transparent vellum that overlay the text, and which relate only occasionally to what is happening in the play.

Antigone, the daughter of ill-fated Oidipus, whose brothers Eteokles and Polyneikes (Carson's own spellings), kill each other in battle, goes against her uncle Kreon's edict to leave Polyneikes unburied, knowingly inviting her punishment of death. She is a heroine who has been interpreted by critics in myriad ways: for Hegel, she represents the ethical value of the family against the state; for George Eliot, the strength of intellect against society; for Anouilh, during the French resistance, the rejection of authority. Woolf viewed her as a proto-feminist; others have called her a terrorist. Carson's cast has known them all: "Remember how Brecht had you do the whole play with a door strapped to your back?" asks the chorus. "We all think you're a grand girl," says Ismene, her sister.

Rather than offering a separate commentary to explain her text, Carson gives her characters their own. "This is Eurydike's monologue it's her only speech in the play," says Kreon's oft-overlooked wife. "You may not know who she is that's OK." She later offers an overview of Antigone's childhood  "we got her the bike we got her a therapist". It's a riff, perhaps, on Judith Butler's investigation into what might have happened had Antigone, rather than Oedipus, been the point of departure for psychoanalysis.

Like AE Housman's parodic "Fragment of a Greek Tragedy" ("ALCMAEON: I journeyed hither a Boetian road. CHORUS: Sailing on horseback, or with feet for oars?"), Antigonick conveys the nonsensical results of most translations of ancient Greek  the banality of stichomythia, the lists of question-words, the improbable coinages. When Kreon enters, he is "rowing his powerboat"  a mix-up of his favorite metaphor, the ship of state; Haemon interrupts an impassioned speech with a footnote: "There is talk there are shadows this girl here I posit a lacuna this girl does not deserve to die."

Readers who are not familiar with ancient Greek texts will most likely feel a bit alienated by all this, but unfamiliarity is, perhaps, the point. Unlike versions of Antigone that try to capture the drama's grandeur (such as Robert Fagles's translation for Penguin) or to make it relevant (including Don Taylor's version, currently at the National Theatre), Carson's aims to show the difficulty of translation, the truly "unbearable" nature of tragedy. The chorus's famous "Ode to Man", in which man is described as able to overcome everything but death, is, in Carson's telling, a bizarre mish-mash of worlds: "Many terribly quiet customers exist but none more / terribly quiet than man / his footsteps pass so perilously soft across the sea  and every Tuesday / down he grinds the unastonishable earth / with horse and shatter  Every outlet works but one / : Death stays dark."

The strangest thing about these lines is their power; even as Carson's translation teeters toward incomprehensibility, it conveys the compression of the ancient Greek, the fraught meaning of deinon (both "terrible" and "wondrous"). It captures, too, the rift between our everyday efforts to keep ourselves busy, and infinite tragedy: that raw nick between Tuesday and death. "You crack me you crack me open you crack me open again," wails Kreon as his fate descends upon him. When all the characters have left the stage, the only person remaining is Nick, "who continues measuring"  which is, after all, the only thing we terribly quiet customers can do.

Sophocles's Antigone is not an obvious comic-book heroine. She has no super-powers, no invisible car and no cape. What she does have, however, is a capacity for generating conflict that rivals that of any S.H.I.E.L.D. employee.

As the daughter of Oedipus and his mother-wife, Jocasta, Antigone comes from cursed stock. As do her brothers, Polynices and Eteocles. When Polynices declares war on Thebes, and both men die, their uncle Creon declares that Eteocles shall receive a proper burial, while Polynices must lie unburied, to be eaten by birds and dogs.

But Antigone believes that natural law  the gods' law  transcends the law of man. Leaving her brother unburied is so utterly wrong that breaking the law to bury him, then being condemned to death herself, is only a minor concern.

Antigone and Creon are both so certain of the rightness of their actions that they are completely intransigent. And this is the story Anne Carson has translated in Antigonick (Nick, for reasons that are unclear, is a mute character, added to the cast by Carson).

The comic-book translation is zingy and modern, packed with references to Hegel and Beckett, which are certain to infuriate traditionalists, but which give it a real punch. When Creon is told that Antigone is the guilty party, he is appalled. "You're the one?" he asks. "Bingo," she replies.

The text is carefully hand-inked by Carson (though a quick spellcheck wouldn't have gone amiss  no city belongs to "it's ruler"). And the pages are interleaved with Bianca Stone's illustrations on vellum that, like the text, vary between the hauntingly beautiful and the unexpectedly funny (Star Trek uniforms don't usually appear in Antigone).

Carson has perfectly captured Antigone's moral fervour and her almost erotic desire for death. The snappiness of her translation hits a different note from Sophocles, but this edition is a treat none the less.