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

Within the context of quantum field theory in curved spacetimes, Hacyan andSarmiento defined the vacuum stress-energy tensor with respect to theaccelerated observer. They calculated it for uniform acceleration and circularmotion, and derived that the rotating observer perceives a flux. Mane relatedthe flux to synchrotron radiation. In order to investigate the relation betweenthe vacuum stress and bremsstrahlung, we estimate the stress-energy tensor ofthe electromagnetic field generated by a point charge, at the position of thecharge. 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 thedivergent contributions by using the expansion of the tensor in powers of thedistance from the point charge. Finally, we take an average for the angulardependence of the expansion. We calculate it for the case of uniformacceleration and circular motion, and it is found that the order of the vacuumstress multiplied by $\pi\alpha$ ($\alpha=e^2/\hbar c$ is the fine structureconstant) is equal to that of the self-stress. In the Appendix, we give anothertrial approach with a similar result.Comment: 25 pages, Submitted to Prog. Theor. Phy