Exact Results in Quantum Theory

The vacuum state of Minkowski space quantum field theory is distinguished as a state of maximal symmetry. General curved spacetimes have no nontrivial symmetry and therefore lack an obvious candidate vacuum state. Nonetheless, one might wonder whether there is still a way of selecting a preferred state. I will discuss various aspects of this issue, describing a general no-go theorem that excludes the existence of a local and covariant choice of preferred state and also results due to Verch and myself, and Brum and Fredenhagen, concerning a recent class of states originally introduced by Afshordi, Aslanbeigi and Sorkin under the name "SJ state", including an extension to Dirac fields in a joint paper with Lang.