 Mode expansion of a Dirac field

ID: mode-expansion-of-a-dirac-field

Codex  0 Created 2026-10-03 Updated 2026-10-05

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}] .

The operators

b^{s}

and

d^{s}

obey fermionic anticommutation relations.

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