New Transformation Equations and the Electric Field Four-vector

11. The Electric Field Four-vector

Our intention, now, is to present the electric field in its most general form and to express the field and force equations and energy-momentum tensor in terms of the generalized electric field. We write the expressions for the components of the generalized electric field four-vector as or, written out,

where the are the components of the potential field four-vector, is the scalar electric potential, and means

We must remember that the signs associated with the terms on the right-hand side of (11.1) are, actually, combination signs reflecting the combination signs in (6.1). Therefore, before performing any operations with (11.1), we must reintroduce these combination signs. From here on, whenever we refer to the electric field four-vector, we will mean the generalized electric field four-vector with components as defined in (11.1), unless otherwise stated.

For a distribution of stationary charges, the components of the electric field four-vector (11.1) reduce to

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