# Dirac equation

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The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. The equation demands the existence of antiparticles and actually predated their experimental discovery. This made the discovery of the positron, the antiparticle of the electron, one of the greatest triumphs of modern theoretical physics.

## Contents

### Mathematical formulation

The Dirac equation in the form originally proposed by Dirac is:

The new elements in this equation are the 4×4 matrices $\alpha_k\,$ and $\,\beta$, and the four-component wavefunction $\,\psi$. The matrices are all Hermitian and have squares equal to the identity matrix: