Relativistic Units

From the definition of 4-vectors shown earlier, we know that

[math]\displaystyle{ \mathbf{R} \equiv \begin{bmatrix} x^0 \\ x^1 \\ x^2 \\ x^3 \end{bmatrix}= \begin{bmatrix} ct \\ x \\ y \\ z \end{bmatrix} \qquad \qquad \mathbf{P} \equiv \begin{bmatrix} p^0 \\ p^1 \\ p^2 \\ p^3 \end{bmatrix}= \begin{bmatrix} \frac{E}{c} \\ p_x \\ p_y \\ p_z \end{bmatrix} }[/math]

The 4-vectors and 4-momenta are defined to be in units of distance and momentum and as such must be multiplied or divided respectively by the speed of light to meet this requirement. For simplicity, the units of c can be chosen to be 1.

DeBroglie's equation

[math]\displaystyle{ E=\hbar \omega \rightarrow \mathbf P=\hbar \mathbf K }[/math]

[math]\displaystyle{ \mathbf{K} \equiv \begin{bmatrix} k^0 \\ k^1 \\ k^2 \\ k^3 \end{bmatrix}= \begin{bmatrix} \frac{\omega}{c} \\ k_x \\ k_y \\ k_z \end{bmatrix} }[/math]