Editing C-symmetry (section)

===Charge conjugation for quantized fields===
The above describes charge conjugation for the single-particle solutions only. When the Dirac field is [[second-quantized]], as in [[quantum field theory]], the spinor and electromagnetic fields are described by operators. The charge conjugation involution then manifests as a [[unitary operator]] <math>\mathcal{C}</math> (in calligraphic font) acting on the particle fields, expressed as<ref>{{harvp|Bjorken|Drell|1964|loc=chapter&nbsp;15}}</ref><ref>{{harvp|Itzykson|Zuber|1980|loc=§&nbsp;3-4}}</ref>

# <math>\psi \mapsto \psi^c = \mathcal{C}\ \psi\ \mathcal{C}^\dagger = \eta_c\ C\ \overline\psi^\textsf{T}</math>
# <math>\overline\psi \mapsto \overline\psi^c = \mathcal{C}\ \overline\psi\ \mathcal{C}^\dagger = \eta^*_c\ \psi^\textsf{T}\ C^{-1}</math>
# <math>A_\mu \mapsto A^c_\mu = \mathcal{C}\ A_\mu\ \mathcal{C}^\dagger = -A_\mu\ </math>

where the non-calligraphic <math>\ C\ </math> is the same 4×4 matrix given before.