Spin Effects in the Electron Structure Functions

The electron structure functions are studied in polarized $e^+e^-$ scattering. The formulae for longitudinally and transversely polarized electrons are presented. The smallnes of the electron mass leads to negligible cross-sections and asymmetries in some cases. Positivity constraints on the structure functions and parton densities are constructed and discussed. The cross-section asymmetries at very high energies, where the inclusion of all elecroweak bosons is necessary, are calculated. Numerical examples, using the asymptotic solutions for the parton densities inside the electron, are presented.