Normalization of Quantized Area Using Torsion and Spin

Abstract

We calculate the change in physical space-time area associated with defects in space-time due to torsion when a particle with spin is present. This change in area is then set equal to the component of the quantized area due to a link of color Pl in the spin network originally calculated by Rovelli and Smolin [6] and shown to have an arbitrary constant factor, the Immirzi parameter, by several authors. Using the usual quantization condition for the square of the spin then allows us to calculate this arbitrary constant factor. We find a well defined expression for the quantized area, \(A = 16\pi l_P^2 \sum \sqrt {j_l (j_l + 1)}\). An interesting picture emerges where a missing link of color Pl in the spin network looks like a torsional defect in space-time associated with a particle of spin jl = Pl/ 2.