# On the Self Energy Correction

1. Aug 14, 2010

### Anamitra

Let us consider the equation E=mc^2 in relation to a charged particle. The traditional deduction of this relation as we find in the introductory texts on Special Relativity do not take into account the huge amount of electrostatic field around it. If the particle annihilates not only the bare mass should produce energy but the electrostatic field should also contribute to the total amount of energy liberated.
In relativistic quantum mechanics the "self energy" is incorporated into the mass of the particle.The virtual photons emerging from the particle come back to hit it,increasing its momentum and thus its energy.This extra energy gets incorporated into the mass of the particle.We must remember that in this consideration the effect of the virtual photons replaces completely the classical field.
Now let us consider an electron and a positron approaching each other.The net field at each point is decreasing and hence the electromagnetic field energy should decrease. Consequently the "electromagnetic mass" should decrease. In the classical sense almost the entire electromagnetic mass gets annihilated before collision takes place.But in actual calculations we consider the annihilation of the self energy simultaneously with that of the bare mass[since self energy is included in the corrected mass].I feel confused here.
From the classical view point we could think of radiation flowing outwards from the approaching charges.Changes in the electric field[due to the approach of the charges] would produce a magnetic field and we could have a Poynting vector carrying energy outwards from the charges. The electron-positron pair may be treated as a "radiating dipole" The loss of electromagnetic mass should get compensated by the flow of radiation.But in such a situation we do not need to induce any correction on the bare mass and annihilation of the electromagnetic field starts long before the annihilation of the bare mass.The concept of E=mc^2,where "m" is the bare mass(and not the corrected mass) should work well in such a situation.

My Queries:1)Which is more appropriate for the relation "E=mc^2"-----the bare mass or the corrected mass?
2)Are the virtual photons a correct and a complete replacement of the classical field?