Electromagnetic Tensor - Definition

Definition

The electromagnetic tensor can be defined using the electromagnetic four-potential:

and its covariant form is found by multiplying by the Minkowski metric η of signature (+,−,−,−) :

where A is the vector potential, ϕ is the scalar potential and c is the speed of light.

The Electric and magnetic fields can be expressed in terms of A and ϕ by:

By definition, the electromagnetic tensor is the exterior derivative of the differential 1-form :

therefore F is a differential 2-form on spacetime. In an inertial frame, the matrices of F read:

F^{\mu\nu} = \begin{bmatrix} 0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & 0 & -B_x \\ E_z/c & -B_y & B_x & 0 \end{bmatrix}

and by lowering indices

F_{\mu\nu} = \begin{bmatrix} 0 & E_x/c & E_y/c & E_z/c \\ -E_x/c & 0 & -B_z & B_y \\ -E_y/c & B_z & 0 & -B_x \\ -E_z/c & -B_y & B_x & 0 \end{bmatrix}

Read more about this topic:  Electromagnetic Tensor

Famous quotes containing the word definition:

    “One definition of man is “an intelligence served by organs.””
    —Ralph Waldo Emerson (1803–1882)

    “The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
    —Ralph Waldo Emerson (1803–1882)

    “I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
    —Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)