---
tag: XNZX7VXXR2
kind: concept
name: Dirac equation
msc: [35Q41, 35Q40]
specializes: [GC5BDZ6QBC]
sources:
  - url: https://en.wikipedia.org/wiki/Dirac_equation
same_as:
  wikidata: Q272621
  wikipedia: Dirac equation
---

## Summary

The Dirac equation is the relativistic wave equation for particles of spin one half, such as the electron.
It is a first-order system for a function with four complex components, and its coefficients are the Dirac matrices, which generate a [[Clifford algebra|A38B1QFK20]].
Each component of a solution solves the [[Klein–Gordon equation|AYCCDQWCJF]], so the Dirac equation is a kind of square root of it.
It predicted antimatter and explains the spin and magnetic moment of the electron.

## Explanations

### L1 human

The Schrödinger equation treats space and time differently, so it does not fit special relativity.
Dirac looked for an equation that is first order in time and in space, like a square root of the relativistic energy relation $E^2 = p^2 + m^2$.
Ordinary numbers cannot do this, so he used $4 \times 4$ matrices whose squares are $\pm 1$ and which anticommute.
The four components of the solution describe the two spin states of the particle and of its antiparticle.