Mode expansion of a Dirac field

The mode expansion of a free Dirac field decomposes it into positive-frequency particle modes and negative-frequency antiparticle modes:

ψ (x) = \sum_{s} \int d Π_{p} [b^{s} (p) u^{s} (p) e^{- i p \cdot x} + d^{s †} (p) v^{s} (p) e^{i p \cdot x}] .

(1)

The operators

b^{s}

and

d^{s}

obey fermionic anticommutation relations.

Table of contents

Antiparticle

 1  0

An antiparticle has the same mass and spin as its particle and opposite additive internal charges. In a relativistic quantum field, antiparticles are created by the negative-frequency part of the field expansion.

Fermionic annihilation operator

 0  0

A fermionic annihilation operator removes one fermion from a specified one-particle mode. Together with its adjoint it satisfies a canonical anticommutation relation such as