Geometric parametrization of SO(D+1) phase space of all dimensional loop quantum gravity

作者：Long, Gaoping^*; Lin, Chun-Yen^*

来源：Physical Review D, 2021, 103(8): 086016.

DOI：10.1103/PhysRevD.103.086016

• COHERENT STATES GCS

To clarify the geometric information encoded in the SO(D + 1) spin-network states for the higher dimensional loop quantum gravity, we generalize the twisted-geometry parametrization of the SU(2) phase space for (1 + 3)-dimensional loop quantum gravity to that of the SO(D + 1) phase space for the all-dimensional case. The Poisson structure in terms of the twisted geometric variables suggests a new gauge reduction procedure, with respect to the discretized gauss and simplicity constraints governing the kinematics of the theory. Endowed with the geometric meaning via the parametrization, our reduction procedure serves to identify proper gauge freedom associated with the anomalous discretized simplicity constraints and subsequently leads to the desired classical state space of the (twisted) discrete Arnowitt-Deser-Misner data.