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Covariant formulation of classical electromagnetism
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<p>The <a href="/facts/Covariance_and_contravariance_of_vectors/s3HGMkhz">covariant</a> formulation of <a href="/facts/Classical_electromagnetism/vK0YI6dj">classical electromagnetism</a> refers to ways of writing the laws of classical electromagnetism (in particular, <a href="/facts/Maxwell%2527s_equations/LfJ1drHS">Maxwell's equations</a> and the <a href="/facts/Lorentz_force/aq1Rc3SS">Lorentz force</a>) in a form that is manifestly invariant under <a href="/facts/Lorentz_transformation/jotJL06G">Lorentz transformations</a>, in the formalism of <a href="/facts/Special_relativity/vsFFc63E">special relativity</a> using rectilinear <a href="/facts/Inertial_frame/1U6TrdG3">inertial coordinate systems</a>. These expressions both make it simple to prove that the laws of classical electromagnetism take the same form in any inertial coordinate system, and also provide a way to translate the fields and forces from one frame to another. However, this is not as general as <a href="/facts/Maxwell%2527s_equations_in_curved_spacetime/ofggksaC">Maxwell's equations in curved spacetime</a> or non-rectilinear coordinate systems. </p>