# Proof that representation of proper orthochronous Poincaré group is unitary

We have defined the action of the representation of the Lorentz group on the Fock space by

$$U(\Lambda)a^*(k_1)\dots a^*(k_N)\Omega = a^*(\Lambda k_1)\dots a^*(\Lambda k_N)\Omega$$.

I am now to proof that this representation is unitary. I have tried by showing that the scalar product is invariant, i.e.

$$(U(\Lambda) a^*(k_1)\Omega, U(\Lambda) a^*(k_2) \Omega) = (a^*(k_1)\Omega, a^*(k_2) \Omega)$$,

but I cannot find any solution with this Ansatz. Is there a better way to show this?