(Optica, 2023) Ortega Gómez, Ángel; Lobet, Michaël; Vázquez Lozano, Juan Enrique; Liberal Olleta, Íñigo; Ingeniería Eléctrica, Electrónica y de Comunicación; Institute of Smart Cities - ISC; Ingeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio Ingeniaritzaren
Time-varying media break temporal symmetries while preserving spatial symmetries
intact. Thus, it represents an excellent conceptual framework to investigate the fundamental
implications of Noether’s theorem for the electromagnetic field. At the same time, addressing
momentum conservation in time-varying media sheds light on the Abraham-Minkowski debate,
where two opposing forms of the electromagnetic field momentum are defended. Here, we present
a tutorial review on the conservation of momentum in time-varying media. We demonstrate
that the Minkowski momentum is a conserved quantity with three independent approaches of
increasing complexity: (i) via the application of the boundary conditions for Maxwell equations
at a temporal boundary, (ii) testing for constants of motion and deriving conservation laws, and
(iii) applying temporal and spatial translations within the framework of the Lagrangian theory of
the electromagnetic field. Each approach provides a different and complementary insight into the
problem.
