The electromagnetic field tensor transforms under this representation.

The matrix form of the field tensor yields the following properties:

These are analogous to two familiar quadratic invariants of the electromagnetic field tensor in classical electromagnetism.

For example, in the case of the gauge group U(1), F will be the electromagnetic field tensor.

Given a field tensor , a scalar called the Lagrangian density can be constructed from and its derivatives.

An alternative unification of descriptions is to think of the physical entity as the electromagnetic field tensor, as described later on.

Electromagnetic field tensor (using a metric signature of + ):

This is called the electromagnetic field tensor, usually written as F. In matrix form:

Physical quantities which can be identified with path curvature include the components of the electromagnetic field tensor.

The first Maxwell equation is satisfied automatically if we define the field tensor in terms of an electromagnetic potential vector .