  A strategy for proving Riemann hypothesis is suggested. The vanishing of the
Rieman Zeta reduces to an orthogonality condition for the eigenfunctions of a
non-Hermitian operator $D^+$ having the zeros of Riemann Zeta as its
eigenvalues. The construction of $D^+$ is inspired by the conviction that
Riemann Zeta is associated with a physical system allowing conformal
transformations as its symmetries. The eigenfunctions of $D^+$ are analogous to
the so called coherent states and in general not orthogonal to each other. The
states orthogonal to a vacuum state (which has a negative norm squared)
correspond to the zeros of the Riemann Zeta. The induced metric in the space
${\cal{V}}$ of states which correspond to the zeros of the Riemann Zeta at the
critical line $Re[s]=1/2$ is hermitian and both hermiticity and positive
definiteness properties imply Riemann hypothesis. Conformal invariance in the
sense of gauge invariance allows only the states belonging to ${\cal{V}}$.
Riemann hypothesis follows also from a restricted form of a dynamical conformal
invariance in ${\cal{V}}$ and one can reduce the proof to a standard analytic
argument used in Lie group theory.
