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Conventional relativistic electrodynamics is set on flat Minkowski spacetime,where all computable quantities are calculated from the flat metric$\eta_{\mu\nu}$. We can redefine the metric of spacetime from the Diracalgebra. In this paper, we study how an electrodynamic interaction can alterthe normal gamma matrix to an effective one and result in a shift in the metricperturbatively. The curvature properties inferred from the curved metric arealso investigated. We also study how the spin operator is changed under theinteraction that contribute to an effective spin operator and how the spin ofan electron will be slightly deviated from $1/2$. Then we perform canonicalquantization of the effective Dirac algebra. Finally we apply our results tothe relativistic hydrogen case and demonstrate how such system curves thespacetime metric.

The effective Dirac algebra by gauge field interaction in relativistic electrodynamics