- #1

jakob1111

Gold Member

- 26

- 17

So... UV divergences arise and thus we need to renormalize, because:

**We have infinite number of degrees of freedom ín a field theory**. (From this perspective, the infinites seem inevitable.)**We multiply fields to describe interactions, fields are distributions and the product of distributions is ill-defined.****We neglect the detailed short-wavelength structure of scattering processes, and the infinites are a result of our approximations with delta potentials.**(From this point of view, the UV divergences aren't something fundamental, but merely a result of our approximation method. )**We are dealing with non-self-adjoint Hamiltonians.**(This is closely related to the 3. bullet point. From this perspective an alternative to the "awkward" renormalization procedure would be the "method of self-adjoint extension".)