and one of these factors is the Dirac equation (see below), upon inserting the energy and momentum operators. For the first time, this introduced new four-dimensional spin matrices α and β in a relativistic wave equation, and explained the fine structure of hydrogen. The solutions to (3A) are multi-component spinor fields, and each component satisfies (1). A remarkable result of spinor solutions is that half of the components describe a particle while the other half describe an antiparticle ; in this case the electron and positron. The Dirac equation is now known to apply for all massive spin- ⁠ 1 / 2 ⁠ fermions. In the non-relativistic limit, the Pauli equation is recovered, while the massless case results in the Weyl equation.