Units

Most often we will work in a natural system of units in which $\hbar = c = 1$. This implies that time has the unit of length, and energy, momentum and mass have units of inverse length.

The final result of any calculation can always be expressed in terms of the dimensionless fine-structure constant $\alpha \approx 1/137.036$. However, this constant is related in different ways to the elementary electric charge, $e$, depending on the units used:

$$\alpha = \left\{ \begin{array}{ll} e^2/\hbar c & \textrm{MK... ...ar c & \textrm{Heaviside-Lorentz system.} \end{array} \right.$$ (2.1)

In the MKSA and Gaussian systems, the electric charge is dimensionless.

When we state definitions or are considering the relative magnitudes of quantities, we will often reintroduced the units. We will most often, but not always, work in the Gaussian system of units.