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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.

Chirality-energy conversion induced by static magnetic effects on free electrons in quantum field theory