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The finite entropy of de Sitter space suggests that in a theory of quantumgravity there are only finitely many states. It has been argued that in thiscase there is no action of the de Sitter group consistent with unitarity. Inthis note we propose a way out of this if we give up the requirement of havinga hermitian Hamiltonian. We argue that some of the generators of the de Sittergroup act in a novel way, namely by mixing in- and out-states. In this way itis possible to have a unitary S-matrix that is finite-dimensional and,moreover, de Sitter-invariant. Using Dirac spinors, we construct a simple toymodel that exhibits these features.Comment: 6 pages, LaTe

De Sitter Space With Finitely Many States: A Toy Story