An anthology of non-local QFT and QFT on non-commutative spacetime

Abstract

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 in the light of previous results on this subject.

Constructive proposals for QFT based on the crossing property and on lightfront holography

“…There is some irony in the fact that Chew and his followers, who tried to find a philosophical basis for their S-matrix bootstrap ideas to attain the status of a theory of everything (TOE), did not succeed in these attempts 7 , whereas 6 One glance at the old conference proceedings and review articles of the Chew S-matrix school reveals that I am not exaggerating. Nowadays the ideological fervor against QFT is hard to understand, in particular in view of the fact that almost all the concepts originated from QFT.…”

“…This idea of giving constructive prominence to "on-shell" aspects is quite different and certainly more conservative than attempts at improving shortdistance properties by introducing non-local interactions in a field theoretic framework (for a historical review of non-local attempts see [6]) which generally causes grave problems with the causality properties underlying particle physics. The main purpose of approaches using scattering concepts ("on-shell") is to avoid such inherently singular objects as pointlike fields in calculational steps, which is a reasonable aim independent of whether one believes that a formulation of interactions in terms of singular pointlike fields exists in the mathematical physics sense or not.…”

“…This poses the interesting question whether by coupling channels which lead to an increasing number of created particles one can approximate field theoretic models by mathematically controllable direct particle interactions. After this interlude about the feasibility of macro-causal relativistic particle theory (for a more detailed presentation see [6]) we now return to the setting of QFT.…”

Jorge A. Swieca’s contributions to quantum field theory in the 60s and 70s and their relevance in present research

“…This No-Go statement should be viewed in the context of a long list of failed attempts to maintain Poincaré invariance without micro-causality [72]. In recent times the nonlocality aspect reappeared in the veil of "noncommutativity" through the backreaction of string theory on QFT.…”

“…Newcomers to QFT notice over short or long that locality is an extremely restrictive requirement, but it is much harder for them to realize that the conceptual problems of physically acceptable relativistic nonlocal theories are even more severe; the idea of constructing consistent models which are just "a little bit non-local" has been one of the most treacherous since the late 50s when physicists became interested in this topic. Poincaré covariance and energy positivity severely limit such a spatial fall-off of the commutator (for a review of attempts at non-locality [72]). For example the commutator cannot decay faster than the Yukawa exponential if one wants to prevent falling back at a local theory.…”