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 formula_118. As it is real, it cannot couple to electromagnetism by itself, but, when complexified, would result in a charged field that transforms as formula_119 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.