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In recent years there has been a great interest in topological photonics andprotected edge states. Here, we present a first principles method to computetopological invariants of three-dimensional gapless phases. Our approach allowsto calculate the topological charges of Weyl points through the efficientnumerical computation of gap Chern numbers, which relies solely on the photonicGreen's function of the system. We particularize the framework to the Weylpoints that are found to emerge in a magnetized plasma due to the breaking oftime reversal symmetry. We discuss the relevance of modelling nonlocality whenconsidering the topological properties of continuous media such as themagnetized plasma. We find that for some of the considered material models thecharge of the Weyl point can be expressed in terms of a difference of the gapChern numbers of two-dimensional material subcomponents. Our theory may beextended to other three-dimensional topological phases, or to Floquet systems.

First principles study of topological invariants of Weyl points in continuous media