Apparaît dans la collection : Resurgence in Mathematics and Physics

Resurgent analysis of the stationary Schrödinger equation (exact-WKB method) has remained exclusively confined to 1D systems due to its underlying linear-ODE techniques. Here, building on a solvable 2D case (a Selberg trace formula, as analyzed with P. CARTIER), and on a Balian-Bloch abstract quantum framework in any dimension using complex orbits, we isolate a very special generalized-heat-trace function as best candidate to start some resurgent description of quantum mechanics in general dimension. The latter statement is still quite embryonic and speculative -our main hope is to encourage future research.