Runaway Solution in QED: A Discussion with Lorenzo

[Sleuth]

HI everybody.
I'm here with a question that I would like to discuss with you.
As you all probably know better than I do, in classical electromagnetism there exists the so called "Runaway solution", i.e. the auto-acceleration of a charged particle.

It is not clear to me how this problem can be seen in QED, and generally speaking in a quantum theory, if it is solved, and if it is not solved.

If i remember well, the runaway solution should be due to the interaction of a charged particle with its e.m. field. But isn't this already included in the "self-energy" of the electron?

and if yes, can we say that renormalization eliminates completely the problem, namely that the inconsistency is cured?

Bye,
Lorenzo

 

[lugita15]

I don't think our knowledge of QED has changed in the past 35 years, so here's a quote from a http://books.google.com/books?id=lS...resnum=3&ved=0CCUQ6AEwAg#v=onepage&q&f=false" which deals with this exact issue:

"How does the same problem look in quantum theory? We do not know [...] But we have never yet succeeded in extracting any information from quantum field theory except in terms of a series in powers of the electron charge. But the problem to which we have been led in the classical case disappears as soon as one expands in a power series. It occurs only in a non-perturbative solution. The question whether the limit implied by the infinite renormalization of quantum electrodynamics would show similar difficulties for a non-perturbative solution, must remain open."