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The electromagnetic tensor, conventionally labelled F, is defined as the exterior derivative of the electromagnetic four-potential, A, a differential 1-form: [1] [2] = . Therefore, F is a differential 2-form— an antisymmetric rank-2 tensor field—on Minkowski space. In component form,
For some materials that have more complex responses to electromagnetic fields, these properties can be represented by tensors, with time-dependence related to the material's ability to respond to rapid field changes (dispersion (optics), Green–Kubo relations), and possibly also field dependencies representing nonlinear and/or nonlocal ...
The electromagnetic stress–energy tensor can be interpreted as the flux density of the momentum four-vector, and is a contravariant symmetric tensor that is the contribution of the electromagnetic fields to the overall stress–energy tensor: = (/ + / / / / / / /), where is the electric permittivity of vacuum, μ 0 is the magnetic ...
An electromagnetic field (also EM field) is a physical field, mathematical functions of position and time, representing the influences on and due to electric charges. [1] The field at any point in space and time can be regarded as a combination of an electric field and a magnetic field .
This is often described by saying that the electric field and magnetic field are two interrelated aspects of a single object, called the electromagnetic field. Indeed, the entire electromagnetic field can be represented in a single rank-2 tensor called the electromagnetic tensor; see below.
The electromagnetic field is a covariant antisymmetric tensor of degree 2, which can be defined in terms of the electromagnetic potential by =.. To see that this equation is invariant, we transform the coordinates as described in the classical treatment of tensors: ¯ = ¯ ¯ ¯ ¯ = ¯ (¯) ¯ (¯) = ¯ ¯ + ¯ ¯ ¯ ¯ ¯ ¯ = ¯ ¯ ¯ ¯ = ¯ ¯ = ¯ ¯.
The algebraic classification of bivectors given above has an important application in relativistic physics: the electromagnetic field is represented by a skew-symmetric second rank tensor field (the electromagnetic field tensor) so we immediately obtain an algebraic classification of electromagnetic fields.
In the tensor calculus formulation, the electromagnetic tensor F αβ is an antisymmetric covariant order 2 tensor; the four-potential, A α, is a covariant vector; the current, J α, is a vector; the square brackets, [ ], denote antisymmetrization of indices; ∂ α is the partial derivative with respect to the coordinate, x α.
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