Canonical Electrodynamics in Ashtekar-Barbero variables

Abstract

We present the full Hamiltonian analysis of electrodynamics, including fermions, photons, and their interaction, on a general curved spacetime in Ashtekar-Barbero variables. Only the time gauge is imposed and the theory is background independent. The details of the constraints of the theory for fermionic and electromagnetic fields coupled to gravity are presented. Moreover, the equations of motion are derived and it is shown that they reduce to the Dirac equation, Maxwell equation and their interaction term in curved or flat spacetime in the appropriate limits. Finally, the behavior of the theory under parity transformation is analyzed. This result presents a suitable foundation for loop or polymer quantization.