  There has been much recent research into possible methods of polarizing an
antiproton beam, the most promising being spin filtering, the theoretical
understanding of which is currently incomplete. The method of polarization
buildup by spin filtering requires many of the beam particles to remain within
the beam after repeated interaction with an internal target in a storage ring.
Hence small scattering angles, where we show that electromagnetic effects
dominate hadronic effects, are important. All spin-averaged and spin-dependent
electromagnetic cross-sections and spin observables for elastic spin 1/2 - spin
1/2 scattering, for both point-like particles and non-point-like particles with
internal structure defined by electromagnetic form factors, are derived to
first order in QED. Particular attention is paid to spin transfer and
depolarization cross-sections in antiproton-proton, antiproton-electron and
positron-electron scattering, in the low | t | region of momentum transfer. A
thorough mathematical treatment of spin filtering is then presented,
identifying the key physical processes involved and highlighting the dynamical
properties of the physical system. We present and solve sets of differential
equations which describe the buildup of polarization by spin filtering in many
different scenarios of interest. The advantages of using a lepton target are
outlined, and finally a proposal to polarize antiprotons by spin filtering off
an opposing polarized electron beam is investigated.
