What is the self energy of electrons and how can it be calculated accurately?

[microtopian]

The following two questions regard the self energy of electrons.. Does anybody know how to start these? I used this site as reference but I wasn't sure if they help with these following questions: http://quantummechanics.ucsd.edu/ph...tes/node44.html

Calculation 1: Pretend the electron is made up of two halves, each with charge e/2. How much energy is required to bring the two halves together, i.e., so that they occupy the same point in space?

Calculation 2: That calculation was a bit over-simplified. Let’s do a better job. Pretend that the charge of an electron is spread uniformly over the surface of a spherical shell with radius r0. Next calculate the electric field everywhere in space, i.e., at an arbitrary distance r from the center of the shell. Obviously the answer will depend on r and r0. Next, calculate the total energy stored in the field, by integrating the energy density u over all space. Finally, let the “electron” become a point particle, by letting r0 go to zero.

 

[StatusX]

If you're you taking the electron to be a point particle, you won't get a finite answer using classical methods. QED resolves this paradox.

 

[pmb_phy]

Assume that you're calculating/observing the energy from the zero momentum frame. You then calculate the energy of the particle's bare mass (the mass that would be there if no charge was present) and then calculate the electrons mass-energy from the expression for energy density of the E-field. The divide the energy by c^2.

When you take the limit r-> 0 you'll get an infinite amount for the energy.

Pete

 

[reilly]

Any graduate level text (Jackson, Panofsky and Phillips) will discuss the self energy problem. Your approaches are not unreasonable, and the last is more-or-less standard in the literature. But the plain fact remains, that in the limit of a point particle, the answer for the energy is infinite. This is true in QED as well. We're talking an unsolved and vexing problem.

Regards,
Reilly Atkinson