12 problems

The Unruh state is a distinguished quantum state for a massless field on a black-hole spacetime, constructed here in the slowly rotating Kerr setting and shown in the source to hav…

Let a scattering matrix act on the state space of a quantum field theory, and call a state smooth with respect to the scattering matrix when its dependence under this action is smo…

Consider the spacetime with an initial globally hyperbolic region and a future Cauchy horizon, and let a linear field theory, or an interacting field theory treated perturbatively,…

In semiclassical gravity, consider gravitational and quantum initial data on an initial surface, and let their Cauchy development be the resulting spacetime and quantum field confi…

Let a globally hyperbolic spacetime be given, and consider the two Proca Hadamard-state conditions referred to as Definition and Definition. Equivalence conjecture. The two definit…

Global Hadamard conjecture. The ground state defined by $G^+$ satisfies this global Hadamard condition.

Let $f\in C_0^\infty(I)$ be a smearing function, where $I\subset\mathbb{R}$ is the domain of conformal time, and consider a scalar field of mass $m$ on a cosmological spacetime wit…

Consider the massless minimally coupled Klein–Gordon field on de Sitter spacetime, and require invariance under the de Sitter boost isometries considered in the paper. De Sitter bo…

Let $mathscr{H}$ be the Hilbert space associated with a stationary Hadamard state, let $K$ be its one-particle structure, and let $SA^R$ and $SB^R$ denote the solution subspaces w…

Let the region of Kruskal spacetime lie to the left of a surface of constant Schwarzschild radius in the right Schwarzschild wedge, with Dirichlet boundary conditions imposed on th…

Let $\mathbf{M}$ be an ultrastatic slab, and let $\omega$ be a pure quasifree state of the Dirac field on $\mathbf{M}$. Suppose that all Wick polynomials of the state have finite f…

The Sorkin–Johnston construction associates states to globally hyperbolic spacetimes by spectrally decomposing the causal propagator restricted to a time interval. A modification i…