Canonical Electrodynamics in Ashtekar-Barbero variables

TL;DR

This paper provides a comprehensive Hamiltonian analysis of electrodynamics with fermions in Ashtekar-Barbero variables on curved spacetime, establishing a foundation for quantum gravity approaches like loop quantum gravity.

Contribution

It offers the full Hamiltonian formulation of coupled fermionic and electromagnetic fields in Ashtekar-Barbero variables without fixing the time gauge, suitable for quantization.

Findings

Derivation of equations of motion reducing to Dirac and Maxwell equations

Explicit constraint analysis for fermions and photons in curved spacetime

Analysis of parity transformation behavior in the theory

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.