AG Mathematische Physik, Beatrice Costeri (Pavia): The Hadamard parametrix on half-Minkowski with Robin boundary conditions: Fundamental solutions and Hadamard states

Abstract: We study the construction of fundamental solutions
and Hadamard states for a Klein-Gordon field in half-Minkowski spacetime
with Robin boundary conditions in d
ge 2 spacetime dimensions. Extending the Robin-to-Dirichlet map of Bondurant and Fulling [J.
Phys. A: Math. Theor. 38 7 (2005)] beyond
the two-dimensional scenario, we express the advanced and retarded
Green operators as convolutions with the inverse map's kernel,
establishing their uniqueness and support properties. We then derive a
local form for the associated Hadamard parametrix that
captures boundary-reflected singularities and we show that our
solutions are consistent with this structure. Finally, we prove that
this local Hadamard condition is equivalent to the global one formulated
via wave-front sets described in terms of generalized
broken bi-characteristics, thus obtaining a Radzikowski-type result for
half-Minkowski spacetime. Based on joint work with C.Dappiaggi, B. A.
Juárez-Aubry and R.D. Singh --
Ann. Henri Poincaré (2026), https://doi.org/10.1007/s00023-026-01702-2.