The cute ghost girl is Natalie Portman of Star Wars fame. You have to wonder how quickly she said yes when a Living Legend called and asked her to be in his music video?
Apparently, Stella has made a number of things for her (including the dress she's wearing in the video). Paul got in touch with Natalie through her and said "Hi, I'm Stella's dad..."
There's several other high profile folks involved as well: the postman is Mackenzie Crook from the original UK version of "The Office" as well as "Pirates of the Caribbean" and the video was directed by Michel Gondry, who also directed "Eternal Sunshine of the Spotless Mind".