Can you run iPad apps on the iPhone 4

[ROFLwaffle]

Well I wanted to get COD Zombies for my iPhone 4 but I saw that it didn't have retina display, then I saw below in the iPad section that it said "Call of Duty Zombies HD" But it's for the iPad. Will i work on my iPhone 4 and will it be in retina display?

[Newgy]

This would actually be good to know. I would like to know if there's anyway that I can recode the Time Magazine App to save me some money on issues