Equivalence between local and global Hadamard States with Robin boundary conditions on half-Minkowski spacetime

29.01.2026, 16:15  –  Building 9, Room 1.22 (Joint session with Analysis group)
Forschungsseminar Differentialgeometrie

Claudio Dappiaggi (Pavia)

We construct the fundamental solutions and Hadamard states for a Klein-Gordon field in half-Minkowski spacetime with Robin boundary conditions in arbitrary dimensions using a generalisation of the Robin-to-Dirichlet map. On the one hand this allows us to prove the uniqueness and support properties of the Green operators. On the other hand, we obtain a local representation for the Hadamard parametrix that provides the correct local definition of Hadamard states, capturing `reflected' singularities from the spacetime timelike boundary. This allows us to prove the equivalence of our local Hadamard condition and the global Hadamard condition with a wave-front set described in terms of generalized broken bi-characteristics, obtaining a Radzikowski-like theorem in half-Minkowski spacetime. 

Joint work with B. Costeri, R. D. Singh and B. Juárez-Aubry -- ArXiv: 2509.26035 [math-ph]