Authors: Ervin Goldfain
It is known that microcausality is a cornerstone principle of relativistic Quantum Field Theory (QFT). It requires commutativity of local fields defined at space-like separations and prohibits physical effects to propagate at superluminal speeds. However, it is also known that the exact localization of quantum fields fails to apply to quantum particles, which behave as non-local entities (the Reeh-Schlieder and Malamert theorems). Over the years, challenges associated with the point-wise description of quantum particles have inspired many attempts to revisit the particle interpretation of QFT. All these proposals suffer from specific limitations and have not gained universal acceptance. Here we suggest that a field theory approaching scale invariance near the fixed points of the Renormalization Group flow blurs the distinction between locality and non-locality. In particular, self-similarity resolves the issue of particle localization in QFT, while reinforcing microcausality by default.
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