Conformal symmetry and quantum localization in space-time

TL;DR

This paper explores how conformal symmetry in quantum field theory enables the definition of quantum space-time observables like position and spin, extending relativistic covariance to quantum regimes.

Contribution

It introduces a framework where conformal symmetries define quantum localization and extends covariance principles to quantum space-time.

Findings

Quantum positions have non-zero commutators related to spin.

Frame transformations differ from classical ones in accelerated frames.

Conformal symmetry extends covariance rules in quantum space-time.

Abstract

The classical procedures which define the relativistic notion of space-time can be implemented in the framework of Quantum Field Theory. Only relying on the conformal symmetries of field propagation, time-frequency transfer and localization lead to the definition of time-frequency references and positions in space-time as quantum observables. Quantum positions have a non vanishing commutator identifying with spin, both observables characterizing quantum localization in space-time. Frame transformations to accelerated frames differ from their classical counterparts. Conformal symmetry nevertheless allows to extend the covariance rules underlying the formalism of general relativity under an algebraic form suiting the quantum framework.