Description
We introduce a Clifford‐algebra method, grounded in group symmetries
and the classical–quantum correspondence, to generate exact solutions
of the Dirac equation. Applying it to an electron vortex beam in a
gravitational plane wave background, we show that the Lorentz boost
from the electron’s rest frame to the laboratory frame carries over
seamlessly from the classical rotor equation to the quantum case. By
exploiting classical analogues—often simpler thanks to symmetry
constraints—we obtain a systematic construction of quantum solutions.
Because gravitational waves mirror electromagnetic plane waves, we
compare our results to Volkov states by defining a “generalized vector
potential” that couples to momentum instead of charge. Despite this
analogy, the gravitational‐wave vortex beam differs markedly from its
electromagnetic counterpart, owing to the fundamentally different
coupling.
