I wasn't thinking that they're physical, just that physicists are used to playing fast and loose with approximations because it's a technique that usually works

I wasn't thinking that they're physical, just that physicists are used to playing fast and loose with approximations because it's a technique that usually works in physics. Or to not really care about what a Dirac distribution really is. Or that defining a tensor (field) as something that transforms like a tensor is a satisfying definition. I am skeptical of the methods that they're used to. But it doesn't look like they're doing that, so I'm probably wrong.