Euclidean LQG dynamics: an electric shift in perspective

Abstract Loop quantum gravity (LQG) is a non-perturbative attempt at quantization of classical phase space description in terms SU (2) connections and electric fields. As emphasized recently Ashtekar Varadarajan (2020 arXiv: 2012.12094 [gr-qc] ), on this space, gravitational evolution time can be understood certain gauge covariant generalizations Lie derivatives with respect to spatial algebra valued vector field called the shift. We present derivation dynamics for Euclidean LQG which informed by understanding. In addition physically motivated nature action Hamiltonian constraint so derived, implies that spin labels regulating holonomies are determined corresponding network state being acted upon thus eliminating ‘spin j -ambiguity’ pointed out Perez. By virtue Thiemann’s seminal work, plays crucial role construction Lorentzian our considerations also have application LQG.