Formulate the non-relativistic expansion in embedding-space momentum-space diagrammatics

Determine how to formulate a non-relativistic expansion within the embedding-space momentum-space framework for worldline diagrammatics in anti-de Sitter spacetime, in order to develop a momentum-space treatment of post-Newtonian interactions complementary to the position-space multipole-resummation approach.

Background

The paper explains that ordinary momentum-space worldline diagrammatics are difficult to formulate in global anti-de Sitter coordinates because coordinate translations are not manifest. It therefore adopts a multipole-expansion and resummation method to derive the near-zone scalar Green function and the resulting post-Newtonian Fokker action.

The authors note that some existing approaches instead use a momentum space inherited from the embedding space. However, the compatibility of that framework with the non-relativistic expansion required for post-Newtonian calculations is left unresolved. Establishing such a formulation would connect the paper’s position-space results to momentum-space methods and potentially to anti-de Sitter scattering and holographic amplitude constructions.