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Resurgent Theta-functions: a conjectured gateway into dimension D superior at 1 quantum mechanics

By André Voros

Appears in 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.

Information about the video

  • Date of recording 12/06/2019
  • Date of publication 15/06/2019
  • Institution IHES
  • Format MP4

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