One of my professors told us this semester, that the 'infinities' that arise in QFT are partly due to the use of the δ-distribution in the commutator relations which read (for fermions)
{Ψ(r′),Ψ†(r)}=δ(r−r′)
In reality we would not have such a δ-distribution but an extended version of it.
Is this view correct? And if definitely yes, is my following view wrong?
As far as I understand it, the δ-distribution is due to the fact that we deal with point particles. If e.g. the electron was an extended particle, then the δ-distribution would be 'finite'.
Since experiments pin down the extension of a particle to R<10−18m it is also likely that the δ-distribution should really be there.
This post imported from StackExchange Physics at 2014-08-07 15:40 (UCT), posted by SE-user physicsGuy