# Dirac Equation

## $\LARGE(i{\hbar}c\gamma^\mu\partial_\mu-mc^2)\psi=0$

### The Terms

$i$ - Imaginary unit $i=\sqrt{-1}$

$\hbar$ - Planck's constant divided by $2\pi$  [Value: 1.051 × 10-34 m2 kg s-1]

$c$ - The speed of light [Value: 3 × 108 m s-1]

$\gamma^\mu$ - Dirac matrices

$\partial_\mu$ - Four-gradient, $\partial_\mu=\left(\frac{1}{c}\frac{\partial}{{\partial}t},\boldsymbol{\nabla}\right)$

$m$ - Rest mass of the electron [Value: 0.511 MeV / c2]

$\psi$ - Wavefunction of the system - the probability amplitude for different configurations of the system at different times. Also known as the quantum state, this is the most complete description that can be given to a physical system.

### What Does It Mean?

The Dirac Equation is a relativistic quantum mechanical wave equation which provides a description of spin-1/2 particles, such as electrons, consistent with quantum mechanics and special relativity. This equation predicts the existence of antiparticles and predates their actual experimental discovery.

### Further information at Warwick

The Dirac Equation is covered in our fourth year modules "PX408 Relativistic Quantum Mechanics" and "PX430 Gauge Theories for Particle Physics".