The charge conjugation symmetry is interpreted as that of electrical charge, because in all three cases (classical, quantum and geometry), one can construct Noether currents 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 A μ μ is interpreted as the 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 frames on the circle. For U(1), this is just the statement that the system is invariant under multiplication by a phase factor e i ϕ ϕ ( x ) that depends on the (space-time) coordinate x . In this geometric setting, charge conjugation can be understood as the discrete symmetry z = ( x + i y ) ↦ ↦ z ¯ ¯ = ( x − − i y ) that performs complex conjugation, that reverses the sense of direction around the circle.