How Does Self Energy Affect the Mass-Energy Equation in Particle Physics?

[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?

 

[eljose79]

I would like to address your queries and provide some insight into the relationship between energy, mass, and the electromagnetic field.

1) In the equation E=mc^2, the "m" represents the total mass of the object, which includes both the bare mass and the mass-energy equivalent of any additional energy, such as the electromagnetic field. Therefore, both the bare mass and the corrected mass are appropriate for the relation. It is important to note that the corrected mass, which takes into account the self-energy of the particle, is a theoretical concept and not a directly measurable quantity.

2) Virtual photons are a theoretical concept used in quantum mechanics to describe the interaction between charged particles. They are not a complete replacement for the classical electromagnetic field, but rather a way of understanding the underlying mechanisms at a subatomic level. The classical field is still a valid concept and is often used in practical applications.

In the case of an electron-positron pair approaching each other, the concept of radiation and the Poynting vector can be applied to understand the energy transfer between the particles. However, it is important to keep in mind that this is a simplified model and does not fully capture the complexities of the interaction at a quantum level.

In conclusion, the equation E=mc^2 remains valid and applicable in both classical and quantum scenarios. The concept of corrected mass and virtual photons are used to better understand and explain the underlying mechanisms, but do not change the fundamental relationship between energy and mass.