Calculation establishes that a quantum positive energy theorem may be possible using a representation based on the Ashtekar connection. Left open is a key question of whether this use of the Ashtekar connection is necessary or whether a positive quantum energy result can be achieved for representations based on other connections, i. e., for [other] values of the Immirzi parameter.

"Positive energy in quantum gravity" arXiv (Jun 10, 2014)