A Fiber Bundle Space Theory of Nonlocal Metamaterials

It is proposed that spacetime is not the most proper space to describe metamaterials with nonlocality. Instead, we show that the most general and suitable configuration space for doing electromagnetic theory in nonlocal domains is a proper function-space infinite-dimensional (Sobolev) vector bundle, a special case of the general topological structure known as fiber bundles. It appears that this generalized space explains why nonlocal metamaterials cannot have unique EM boundary conditions at interfaces involving spatially dispersive media.