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Confrontation of symmetries
This document discusses noncommutative quantum field theory and quantizing space-time. It introduces additional uncertainty relations for coordinates due to potential black hole formation from measurements at small distances. It then summarizes approaches to quantizing space-time from string theory and other models. The implementation takes noncommutativity between coordinate operators, preserving translational invariance but breaking Lorentz symmetry to SO(1,1)xSO(2). Twisted Poincare algebra is discussed as an actual symmetry of the theory.