In physics literature, a transformation such as C : ϕ ϕ ↦ ↦ ϕ ϕ c = − − ϕ ϕ might be written without any further explanation. The formal mathematical interpretation of this is that the field ϕ ϕ is an element of R × × Z 2 where Z 2 = { + 1 , − − 1 } . Thus, properly speaking, the field should be written as ϕ ϕ = ( r , c ) which behaves under charge conjugation as C : ( r , c ) ↦ ↦ ( r , − − c ) . It is very tempting, but not quite formally correct to just multiply these out, to move around the location of this minus sign; this mostly "just works", but a failure to track it properly will lead to confusion.