There are a number of functions where some limit will take you to a Dirac delta.

Lorenzian,Gaussian etc.

Also has integral representation, most

useful in Fourier Analisis.

As to the relevance for a model for an electron say, i would say this is dubious.

Juan Weisz This is actually not correct. You can see the proofs in section 3. Preprint THE FRAMEWORK OF EVERYTHING (FOE)

there is no such thing as a point particle, it is just a generalization to simplify calculations, nothing more. as for delta, all limits at zero, infinitesimal, and infinity, simultaneously. calc 101 is just engineering simplifications, not theoretical mathematics.

William Bray Point particles are certainly the idealized case in many theories but not all. For example, zero-branes in M-Theory are zero dimensional. I am not clear on what the rest of your comment says.

@russell smith, zero branes and m theory are theoretical, not real entities.

no real thing can be a zero dimensuonal point. limits go to infinty when you divide by zero, to zero when you multiply by zero, or zero divided by a real number.

brane theories are offshoots of Quantum Field Theory, which ignores infinity and infinitesimals arbitrarily: eg, just a theory, 'what if.'

William Bray "If it were determined that 0-branes cannot exist, researchers might need to revise M-theory or develop alternative frameworks that do not rely on the existence of 0-branes. This could involve focusing on higher-dimensional branes or exploring other aspects of the theory that remain valid." This would imply that zero-branes are believed to exist within the context of M-Theory. Let me know if I am mistaken.

QFT is quite amazing, but I think that the concept of the FE stated in my article resolves the ontological issues that it has. In order to do this you have to first prove that certain types of particles can't exist regardless of if some interprations of physics suggest that they do or not.