Study of spin states in vacuum pair production via the Dirac-Heisenberg-Wigner formalism

A general spin-resolved momentum distribution of electron-positron pairs produced in strong external fields is derived by combining the covariant spin projection operator and the Dirac-Heisenberg-Wigner (DHW) formalism. The result shows that the spin-resolved and helicity-resolved momentum distributions given in previous literature are actually two special cases of it. For any spin-direction unit vector, numerical investigations demonstrate that when the $z$-component of the unit vector vanishes, the number density of produced spin-up and spin-down particles is equal, while their momentum distributions have some asymmetry. For a nonzero $z$-component of the unit vector, there is a difference of $1-3$ orders of magnitude in the number density of spin-up and spin-down particles induced by angular momentum transfer in multiphoton absorption. Moreover, as the electric field strength increases and/or the field frequency decreases, the asymmetry between the spin-up and spin-down particle number density decreases rapidly. These results offer an approach to study general spin states in vacuum pair production, and enhance our understanding of angular momentum transfer from fields to matter in extreme environments.