A Calculation on the Self-field of a Point Charge and the Unruh Effect

TL;DR

This paper investigates the relationship between the vacuum stress-energy tensor and the electromagnetic self-field of a point charge under uniform acceleration and circular motion, revealing proportionality between vacuum stress and self-stress.

Contribution

It introduces a method to estimate the electromagnetic stress-energy tensor of a point charge's self-field, linking it to the vacuum stress in accelerated frames.

Findings

Vacuum stress is proportional to the self-stress of a point charge.

The order of vacuum stress times πα matches the self-stress for specific motions.

A new approach confirms the proportionality between vacuum stress and self-stress.

Abstract

Within the context of quantum field theory in curved spacetimes, Hacyan and Sarmiento defined the vacuum stress-energy tensor with respect to the accelerated observer. They calculated it for uniform acceleration and circular motion, and derived that the rotating observer perceives a flux. Mane related the flux to synchrotron radiation. In order to investigate the relation between the vacuum stress and bremsstrahlung, we estimate the stress-energy tensor of the electromagnetic field generated by a point charge, at the position of the charge. We use the retarded field as a self-field of the point charge. Therefore the tensor diverges if we evaluate it as it is. Hence we remove the divergent contributions by using the expansion of the tensor in powers of the distance from the point charge. Finally, we take an average for the angular dependence of the expansion. We calculate it for the case of uniform acceleration and circular motion, and it is found that the order of the vacuum stress multiplied by $\pi\alpha$ ($\alpha=e^2/\hbar c$ is the fine structure constant) is equal to that of the self-stress. In the Appendix, we give another trial approach with a similar result.