Relativistic Planck-scale polymer. (English) Zbl 1380.83086
Summary: 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. Here, we 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.
MSC:
| 83C45 | Quantization of the gravitational field |
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