Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

For electromagnetic field theories, canonical energy-momentum conservation laws can be derived from the underpinning spacetime translation symmetry according to Noether procedure. However, tensors (EMTs) are neither symmetric nor gauge-symmetric (gauge invariant). The Belinfante-Rosenfeld (BR) method is a well-known procedure symmetrize EMTs, which also renders them gauge for first-order theories. High-order theories appear in study of gyrokinetic systems magnetized plasmas and Podolsky system radiation reaction classical charged particles. these high-order EMTs not necessarily vice versa. In present study, we develop new gauge-symmetrization carried out using Faraday tensor ${F}_{\ensuremath{\mu}\ensuremath{\nu}}$, instead 4-potential ${A}_{\ensuremath{\mu}}$, derive EMT ${T}_{\mathrm{N}}^{\ensuremath{\mu}\ensuremath{\nu}}$. We show that gauge-dependent part ${T}_{\mathrm{N}}^{\ensuremath{\mu}\ensuremath{\nu}}$ removed displacement-potential ${\mathcal{F}}^{\ensuremath{\sigma}\ensuremath{\mu}\ensuremath{\nu}}\ensuremath{\equiv}{\mathcal{D}}^{\ensuremath{\sigma}\ensuremath{\mu}}{A}^{\ensuremath{\nu}}/4\ensuremath{\pi}$, where ${\mathcal{D}}^{\ensuremath{\sigma}\ensuremath{\mu}}$ antisymmetric electric displacement tensor. This gauge-symmetrizes without making it symmetric, adequate applications involving general relativity. such as standard Maxwell system, ${\mathcal{F}}^{\ensuremath{\sigma}\ensuremath{\mu}\ensuremath{\nu}}$ reduces familiar BR superpotential ${\mathcal{S}}^{\ensuremath{\sigma}\ensuremath{\mu}\ensuremath{\nu}}$, developed used simpler calculate ${\mathcal{S}}^{\ensuremath{\sigma}\ensuremath{\mu}\ensuremath{\nu}}$ employing angular momentum 4D spacetime. When coupled particles, shown effective well.