  Magnetic effects on free electron systems have been studied extensively in
the context of spin-to-orbital angular momentum conversion. Using a quantum
field theory framework, we derive a similar relationship in the
non-relativistic limit for the energy of electrons with momentum directed along
the axis of a spatiotemporally constant, weak magnetic field. For a single
electron the expectation value of the maximum energy shift, which is fixed by
our defined chirality index of the electron state, is computed perturbatively
to first order as about 15% of the electron rest mass. This effect is orders of
magnitude larger than that predicted by the quantum mechanical Zeeman shift. We
then show, in the low-mass approximation, an analogous conversion between
energy and chirality for a system of free electrons and suggest possible
experimental tests of this phenomenon in electron states encountered across
multiple physics disciplines.
