Notation

NOTATION

Three-dimensional quantities

Three-dimensional tensor indices are denoted by Greek letters

Element of volume, area and length: $dV$ , $d\mathbf{f}$ , $d\mathbf{l}$

Momentum and energy of a particle: $\mathbf{p}$ and $\mathcal{E}$

Hamiltonian function: $\mathcal{H}$

Scalar and vector potentials of the electromagnetic field: $\phi$ and $\mathbf{A}$

Electric and magnetic field intensities: $\mathbf{E}$ and $\mathbf{H}$

Charge and current density: $\rho$ and $\mathbf{j}$

Electric dipole moment: $\mathbf{d}$

Magnetic dipole moment: $\mathbf{m}$

Four-dimensional quantities

Four-dimensional tensor indices are denoted by Latin letters $i, k, l, \dots$ and take on the values 0, 1, 2, 3

We use the metric with signature $(+---)$

Rule for raising and lowering indices—see p. 14

Components of four-vectors are enumerated in the form $A^i = (A^0, \mathbf{A})$

Antisymmetric unit tensor of rank four is $\epsilon^{iklm}$ , where $\epsilon^{0123} = 1$ (for the definition, see p. 17)

Element of four-volume $d\Omega = dx^0 dx^1 dx^2 dx^3$

Element of hypersurface $dS^i$ (defined on pp. 20–21)

Radius four-vector: $x^i = (ct, \mathbf{r})$

Velocity four-vector: $u^i = dx^i/ds$

Momentum four-vector: $p = (\mathcal{E}/c, \mathbf{p})$

Current four-vector: $j^i = (c\rho, \rho\mathbf{v})$

Four-potential of the electromagnetic field: $A^i = (\phi, \mathbf{A})$

Electromagnetic field four-tensor $F_{ik} = \frac{\partial A_k}{\partial x^i} - \frac{\partial A_i}{\partial x^k}$ (for the relation of the components of

$F_{ik}$ to the components of $\mathbf{E}$ and $\mathbf{H}$ , see p. 65)

Energy-momentum four-tensor $T^{ik}$ (for the definition of its components, see p. 83)