Quantum fields, non-locality and quantum group symmetries

TL;DR

This paper explores how small deviations from locality in quantum fields, caused by quantum gravity effects, lead to the emergence of quantum group symmetries instead of traditional Lie algebra symmetries, providing insights into quantum gravity models.

Contribution

It demonstrates that quantum gravity-induced non-locality results in space-time symmetries described by quantum groups rather than Lie algebras, offering an intuitive understanding of deformed symmetries in quantum gravity.

Findings

Symmetries become non-co-commutative Hopf algebras under non-locality.

Quantum groups naturally arise as low-energy limits of quantum gravity models.

Provides a mechanism for the emergence of deformed co-products in quantum relativistic symmetries.

Abstract

We study the action of space-time symmetries on quantum fields in the presence of small departures from locality determined by dynamical gravity. It is shown that, under such relaxation of locality, the symmetries of the theory cannot be described within the usual framework of Lie algebras but rather in terms of non-co-commutative Hopf algebras or "quantum groups". Similar "quantizations" of space-time symmetries are expected to emerge in the low-energy limit of certain quantum gravity models and have been used to describe the symmetries of various non-commutative space-times. Our result provides an intuitive characterization of the mechanism that could lead to the emergence of deformed co-products in models of quantum relativistic symmetries.