Medusa, Antaeus, and Caesar Libycus

Although it is well known that Lucan’s Libya is a wild and threatening place, its threat is not restricted to indigenous people, places and things, such as Hannibal, Cleopatra, the Syrtes, or the desert with its catalogue of horrifying snakes. He also associates Libya with anti-Republican Romans, above all Julius Caesar, who endangers the Republic with his excessive, animalistic energy and resembles the continent where he is trapped in the final book. Although the gods as characters are removed from the world of the Bellum Civile, Lucan allows supernatural traces to linger in particular locations such as the Gallic grove in Book 3 or Thessaly in Book 6. Libya is by far the greatest of these reservoirs of frightening myth and fantasy, which do violence to the historical credibility of the narrative, just as Libya itself is presented as the origin or conduit of a number of historical characters who assault Italy and Europe. Lucan’s two mythic narratives (Antaeus in Book 4 and Medusa in Book 9) are essential parts of the hostile Libyan landscape, but in very different ways. The male Antaeus, associated with lions, is connected with a region of solid rock where he was destroyed. The female Medusa, associated with snakes, is connected with a region of shifting sands where she left a deadly, everlasting legacy. To complicate matters further, even though Medusa’s snakes represent the annihilation of the Republican self, the logic of the narrative is undermined and there is even a sympathetic subtext. As part of Libya’s historical and mythical legacy, these stories reveal that for Lucan, historical epic is linked with Republicanism, but mythical epic is in the service of dictatorship.

Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.