  The quantum Jarzynski equality is an important theorem of modern quantum
thermodynamics. We show that the Jarzynski equality readily generalizes to
relativistic quantum mechanics described by the Dirac equation. After
establishing the conceptual framework we solve a pedagogical, yet
experimentally relevant, system analytically. As a main result we obtain the
exact quantum work distributions for charged particles traveling through a
time-dependent vector potential evolving under Schr\"odinger as well as under
Dirac dynamics, and for which the Jarzynski equality is verified. Special
emphasis is put on the conceptual and technical subtleties arising from
relativistic quantum mechanics.
