One of my professors told us this semester, that the 'infinities' that arise in QFT are partly due to the use of the $\delta$-distribution in the commutator relations which read (for fermions)

$\left\{\Psi(r'), \Psi^\dagger(r)\right\} = \delta(r-r')$

In reality we would not have such a $\delta$-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 $\delta$-distribution is due to the fact that we deal with point particles. If e.g. the electron was an extended particle, then the $\delta$-distribution would be 'finite'.

Since experiments pin down the extension of a particle to $R < 10^{-18}m$ it is also likely that the $\delta$-distribution should really be there.

This post imported from StackExchange Physics at 2014-08-07 15:40 (UCT), posted by SE-user physicsGuy