The above describes the conventional construction of a charged scalar field. It is also possible to introduce additional algebraic structure into the fields in other ways. In particular, one may define a "real" field behaving as C : ϕ ϕ ↦ ↦ − − ϕ ϕ . As it is real, it cannot couple to electromagnetism by itself, but, when complexified, would result in a charged field that transforms as C : ψ ψ ↦ ↦ − − ψ ψ ∗ ∗ . Because C-symmetry is a discrete symmetry, one has some freedom to play these kinds of algebraic games in the search for a theory that correctly models some given physical reality.