An anthology of non-local QFT and QFT on noncommutative spacetime Dedicated to Detlev Buchholz on the occasion of his 60th birthday

Ever since the appearance of renormalization theory there have been several differently motivated attempts at non-localized (in the sense of not generated by point-like fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review of contemporary ideas in the light of previous results on this subject. 1 History of attempts at non-local fields To attribute in-depth investigations of non-local QFT to the last decade, as it is done in most contemporary articles 0n this subject, is historically incorrect; there was already a flurry of interest (quite a strong one considering the number of particle physicist at that time) in non-local aspects of QFT leading to significant results as far back as the late 50s. This interest in non-local aspects originated in the wake of renormalization of QED and of the LSZ scattering theory. The main physical motivating idea was to get to more and ”better” (in the sense of less singular) interactions by using L-invariant structure functions in the interaction part of the Lagrangian. In addition there was the desire to understand whether (pre-QCD) meson-nucleon structure, as it became experimentally accessible in nucleon formfactors, could be consistently used in a Lagrangian formalism; in other words if what nowadays would be considered This is of course ment relative to the much smaller number of particle physicists at that time.