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.
Relativistic Planck-scale polymer / AMELINO CAMELIA, Giovanni; Arzano, Michele; Da Silva, Malú Maira; Orozco-Borunda, Daniel H.. - In: PHYSICS LETTERS. SECTION B. - ISSN 0370-2693. - 775:(2017), pp. 168-171. [10.1016/j.physletb.2017.10.071]
Relativistic Planck-scale polymer
AMELINO CAMELIA, Giovanni;Arzano, Michele;
2017
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.