Renormalization in string-localized field theories: a microlocal analysis

Christian Gaß
July 27, 2021
Using methods of microlocal analysis, we prove that renormalization stays a pure ultraviolet problem in string-localized field theories, despite the weaker localization. Thus, power counting does not lose its significance as an indicator for renormalizability. Our proof puts the conjecture that the good ultraviolet behavior of string-localized fields improves renormalizability on safe mathematical ground. It also follows that the standard renormalization methods can be employed for string-localized field theories without any major adjustments.

string localized quantum fields, microlocal analysis