Photon angular momentum near Planck scale

TL;DR

This work develops a covariant gauge theory under the Relativistic Generalized Uncertainty Principle (RGUP), introducing a minimal-length deformation $\gamma$ that modifies the Maxwell sector with a higher-derivative term $F^{\mu\nu}\Box F_{\mu\nu}$. Using Noether's theorems, it derives both the canonical and Belinfante energy-momentum tensors and constructs the RGUP-modified angular-momentum currents, showing that orbital and spin densities are not independently conserved but the total angular momentum remains conserved under Lorentz symmetry. The authors provide explicit RGUP-corrected expressions for the angular-momentum densities and the Poynting vector, illustrating how Planck-scale kinematics redistribute energy-momentum flow while recovering standard Maxwell results in the $\gamma\to0$ limit. Although the framework is formally consistent and Lorentz-covariant, it currently lacks quantitative bounds on $\gamma$ and does not include interactions with charged matter or gravity; future work is planned to extract phenomenological constraints and extend to realistic media and gravitational backgrounds.

Abstract

We study the angular momentum structure of the gauge field in Lorentz covariant relativistic generalized uncertainty principle (RGUP) framework incorporating Planck scale minimal length effects. Using Noether's theorem for higher derivative RGUP-modified gauge field Lagrangian, we obtain the canonical and symmetric (Belinfante) energy-momentum tensors and the corresponding gauge spin and orbital angular momentum currents. We show that the canonical and Belinfante-Rosenfeld angular-momentum tensors continue to satisfy the standard conservation law in the presence of Planck-scale corrections. %These results support the stability of fundamental conservation laws under high-energy modifications. The RGUP corrections introduce higher-order contributions to the angular momentum density and momentum flow, yielding a modified Poynting vector, with the Maxwell limit recovered for vanishing RGUP parameter.