Troublesome infinities in physics

[Akater]

Hello,

it is said that physicists sometimes need to multiply two generalized functions (square Dirac delta, for example) which makes little sense from the mathematical viewpoint. Could you please provide some examples where such an issue occurs?

Actually, I would be happy to see examples of two different kinds,

— those where (an empirical / magical) physically consistent solution is known;

— those which are still open problems.

I'd like to really understand the physics behind equations (their derivations, at least), but my physical background is not solid. So, please, if possible, don't stick to QFT problems. Classical mechanics / field theory / waves would be perfect. (Although, some example is definitely better than no example at all.)

________
Sorry for poor English.

 

[Eynstone]

All such 'generalised' functions can be reformulated with mathematical rigour. The Dirac delta 'function', for instance, is really the Dirac delta functional.

 

[Akater]

Sure. I was talking about (supposed) situation when physicist need to multiply them and experience problems with the multiplication operation.