Bounds on the Polymer Scale from Gamma Ray Bursts

The polymer representations, which are partially motivated by loop quantum gravity, have been suggested as alternative schemes to quantize the matter fields. Here we apply a version of the polymer representations to the free electromagnetic field, in a reduced phase space setting, and derive the corresponding effective (i.e., semiclassical) Hamiltonian. We study the propagation of an electromagnetic pulse and we confront our theoretical results with gamma ray burst observations. This comparison reveals that the dimensionless polymer scale must be smaller than $4\times 10^{-35}$, casting doubts on the possibility that the matter fields are quantized with the polymer representation we employed.