The Barbero–Immirzi Parameter: An Enigmatic Parameter of Loop Quantum Gravity

The Barbero-Immirzi parameter ($\gamma$) is introduced in loop quantum gravity (LQG) whose physical significance still a biggest open question; because of its profound traits. In some cases, it real-valued; while, complex-valued other cases. This emerges out the process denoting Lorentz connection with non compact group $SO(3,1)$ form complex values rotations, either $SO(3)$ or $SU(2)$. Initially, was appeared Ashtekar variables. Fernando Barbero proposed possibility to include within formalism. Its present value fixed by counting micro states and matching semi classical black hole entropy computed Stephen Hawking. used count size area Planck units. Until, discovery spectrum operator LQG; remains unknown. However, complete yet be explored. article, an introduction LQG, time line this research area, various proposals regarding are given.