The boundary is mixed

We show that in Oeckl’s boundary formalism the boundary vectors that do not have a tensor form represent, in a precise sense, statistical states. Therefore the formalism incorporates quantum statistical mechanics naturally. We formulate general-covariant quantum statistical mechanics in this language. We illustrate the formalism by showing how it accounts for the Unruh effect. We observe that the distinction between pure and mixed states weakens in the general covariant context, suggesting that local gravitational processes are naturally statistical without a sharp quantal versus probabilistic distinction.