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Paul Dirac sought a relativistic quantum mechanics whose evolution equation remained first order in both time and spatial derivatives. A free-particle Hamiltonian $H=c\mathbf{\alpha }\cdot \mathbf{p}+\beta m{c}^2$ reproduces the relativistic relation $H^2=c^2{\mathbf{p}}^2+m^2{c}^4$ when its coefficient matrices satisfy suitable anticommutator identities. The required multi-component wave function incorporates electron spin within the relativistic dynamics. His 1928 paper used this construction to address the doubling of atomic states that earlier theories had treated by adding spin separately.^[ref]

A physicist who developed a relativistic theory of the electron. He shared the Nobel Prize in Physics in 1933 with Erwin Schrödinger.^[ref]