# CFT in momentum space

Is there a way to see the conformal symmetry in momentum space in a CFT? I mean if I can recover the conformal group in some way in momentum space.

• This paper should be helpful. – MannyC Apr 26 '19 at 3:48

The generator of special conformal transformation act, schematically, as $$K\sim x^2\partial_x+x\partial_x.$$ In momentum space this becomes $$K\sim p\partial_p^2+p\partial_p.$$ Since $$K$$ is a second order differential operator, $$e^{\lambda K}$$ does not act in a local, geometrical way on functions.