Editing C-symmetry (section)

=== In classical fields ===
The charge conjugation symmetry is interpreted as that of [[electrical charge]], because in all three cases (classical, quantum and geometry), one can construct [[Noether current]]s that resemble those of [[classical electrodynamics]]. This arises because electrodynamics itself, via [[Maxwell's equations]], can be interpreted as a structure on a [[U(1)]] [[fiber bundle]], the so-called [[circle bundle]]. This provides a geometric interpretation of electromagnetism: the [[electromagnetic potential]] <math>A_\mu</math> is interpreted as the [[Connection (mathematics)|gauge connection]] (the [[Ehresmann connection]]) on the circle bundle. This geometric interpretation then allows (literally almost) anything possessing a complex-number-valued structure to be coupled to the electromagnetic field, provided that this coupling is done in a [[gauge-invariant]] way. Gauge symmetry, in this geometric setting, is a statement that, as one moves around on the circle, the coupled object must also transform in a "circular way", tracking in a corresponding fashion. More formally, one says that the equations must be gauge invariant under a change of local [[coordinate frame]]s on the circle. For U(1), this is just the statement that the system is invariant under multiplication by a phase factor <math>e^{i\phi(x)}</math> that depends on the (space-time) coordinate <math>x.</math>  In this geometric setting, charge conjugation can be understood as the discrete symmetry <math>z = (x + iy) \mapsto \overline z = (x - iy)</math> that performs complex conjugation, that reverses the sense of direction around the circle.