QFT, EFT and GFT

We explore the correspondence between geometric function theory (GFT) and quantum field (QFT). The crossing symmetric dispersion relation provides necessary tool to examine connection GFT, QFT, effective theories (EFTs), enabling us connect with crossing-symmetric EFT-hedron. Several existing mathematical bounds on Taylor coefficients of Typically Real functions are summarized shown be enormous use in bounding Wilson context 2-2 scattering. prove that two-sided guaranteed exist quite generally for fully situation. Numerical implementation GFT constraints (Bieberbach-Rogosinski inequalities) is straightforward allows a systematic exploration. A comparison our findings obtained using techniques other results literature made. study both three-channel as well two-channel cases, latter having some crucial differences. also consider bound state poles massless EFTs. Finally, we nonlinear arising from positivity certain Toeplitz determinants, which occur trigonometric moment problem.