Analyticity at larger coupling and optimal convergence radii

Establish analyticity of ground states and ground-state energies for massless bosonic quantum-field models at larger coupling constants, determine their radii of convergence, and ascertain whether those radii reach the corresponding physical coupling values.

Background

The introduction identifies a gap in existing analyticity results for models coupled to massless bosonic fields. Although prior approaches establish analyticity in regimes of small coupling constants, the behavior at larger couplings and the precise size of the convergence domain remain unresolved in the cited literature.

The problem concerns both mathematical control of analytic continuation and the physical relevance of perturbative expansions: determining whether the convergence radius reaches actual physical parameter values would rigorously validate perturbative calculations in physically meaningful regimes.

References

Establishing analyticity for larger coupling and determining the radius of convergence—and whether it reaches actual physical values—remain open problems.

— Holomorphy of the ground state and energy for bosonic quadratic Hamiltonians  (2608.27862 - Imura et al., 28 Aug 2026) in Section 1, Introduction, p. 2

Conjecture 5.10. The radii of convergence of the Maclaurin series for the ground state and its energy are finite values strictly greater than Q.

— Holomorphy of the ground state and energy for bosonic quadratic Hamiltonians  (2608.27862 - Imura et al., 28 Aug 2026) in Conjecture 5.10, Section 5.2.2, p. 27