# Are the ideals in two GNS constructions linked to the equivalence (or not) of the CCR representations?

Starting from the abstract C* algebra $$A$$ of canonical commutative relations, a state $$\rho$$ over this algebra enables to construct a Hilbert space $$A/I$$ where $$I$$ is the ideal of the elements $$a$$ such that $$\rho (a^* a) = 0$$. the vacuum in this space depends on the equivalence class of $$\rho$$. I read that in the case of infinite degrees of freedom, many inequivalent representations can be built by this construction. I wonder how the inequivalence of the representations depends on properties of these ideals (or not).