Abstract
We present new, nontrivial generalizations of the recent Tomaras-Tsamis-Woodard extension of the original Schwinger formula for charged pair production in a constant electric field. That extension generalized the Schwinger result to electric fields dependent upon one or the other light-cone coordinates, or the present work generalizes their result to electric fields dependent upon both coordinates. Displayed in the form of a final, functional integral, or equivalent linkage operation, our result does not appear to be exactly calculable in the general case; and we give a simple, approximate example when is a slowly varying function of its variables. We extend this result to the more general case where can point in a varying direction, and where an arbitrary magnetic field is present; both extensions can be cast into the form of Gaussian-weighted functional integrals over well defined factors, which are amenable to approximations depending on the nature and variations of the fields.
- Received 6 August 2002
DOI:https://doi.org/10.1103/PhysRevD.67.016003
©2003 American Physical Society