Authors: Brian Slovick
In the conventional approach of renormalization, divergent loop integrals are regulated and combined with counterterms to satisfy a set of renormalization conditions. While successful, the process of regularization is tedious and must be applied judiciously to obtain gauge-invariant results. In this Letter, I show that by recasting the renormalization conditions as the initial conditions of momentum-space differential equations for the loop amplitudes, the need for regularization disappears because the process of differentiating under the loop integrals renders them finite. I apply this approach to successfully renormalize scalar $\phi^4$ theory and QED to one-loop order without requiring regularization or counterterms. Beyond considerable technical simplifications, the ability to perform renormalization without introducing a regulator or counterterms can lead to a more fundamental description of quantum field theory free of ultraviolet divergences.
Comments: 5 Pages.
Unique-IP document downloads: 56 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.