Generalised Sorkin-Johnston and Brum-Fredenhagen States for Quantum Fields on Curved Spacetimes

The presented work contains a new construction of a class of distinguished quasifree states for the scalar field and Proca field on globally hyperbolic spacetimes. Our idea is based on the axiomatic construction of the Sorkin-Johnston (SJ) state \cite{Sorkin:2017fcp}; we call these states \emph{generalised SJ states}. We give a concrete application of this framework with the construction of the `thermal' SJ state. By slightly modifying the construction of generalised SJ states, we also introduce a new class of Hadamard states, which we call \emph{generalised SJ states with softened boundaries}. We show when these states satisfy the Hadamard condition and compute the Wick polynomials. Finally we construct the SJ and Brum-Fredenhagen (BF) states for the Proca field on ultrastatic slabs with compact spatial sections. We show that the SJ state construction fails for the Proca field, yet the BF state is well defined and, moreover, satisfies the Hadamard condition.