evaluation - Overloading conjugate operator for a particular function

I trying to modify the behaviour of the built-in Conjugate[] operator on a particular function I have defined, to take into account that some of its variables are real.

ClearAll[f];
f /: Conjugate[f[k_]] := Conjugate[F[r]] Exp[I k r]

f[k_] := F[r] Exp[-I k r]

The problem with using UpValues in this way is that the DownValues for f[k] are evaluated before, resulting in:

Conjugate[f[k]]=Exp[I Conjugate[k r]] Conjugate[F[r]]

Using non-standard evaluation seems to do the trick

Conjugate[Unevaluated[f[k]]]=Exp[I k r] Conjugate[F[r]]

However, I want to use my function inside expressions like

f[k1] + f[k2] + Conjugate[f[k3]]

without having to manually replace f[_] by Unevaluated[f[_]].

Answer

One possibility would be to define a new Conjugate function, myConjugate, the behaves in the same way as Conjugate, except when it encounters a phase of the type Exp[+(-)I k r], it transforms it to Exp[-(+)I k r], leaving k and r as real variables.

Another possibility (and the one I ended up using) is to go along the lines of this stack overflow answer and use UpValues to explicitly define k and r as being real:

ClearAll[makeReal];
makeReal[a__Symbol] := (# /: Conjugate[#] := #) & /@ List[a]

makeReal[k, r]

Then one gets the expected

Conjugate[F[r] Exp[-I k r]]= Exp[I k r] Conjugate[F[r]]

Comments

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