  Polymer quantum mechanics has been studied as a simplified picture that
reflects some of the key properties of Loop Quantum Gravity; however, while the
fate of relativistic symmetries in Loop Quantum Gravity is still not
established, it is usually assumed that the discrete polymer structure should
lead to a breakdown of relativistic symmetries. We here focus for simplicity on
a one-spatial-dimension polymer model and show that relativistic symmetries are
deformed, rather than being broken. The specific type of deformed relativistic
symmetries which we uncover appears to be closely related to analogous
descriptions of relativistic symmetries in some noncommutative spacetimes. This
also contributes to an ongoing effort attempting to establish whether the
"quantum-Minkowski limit" of Loop Quantum Gravity is a noncommutative
spacetime.
