We perform a complete, mathematically rigorous analysis of static, spherically symmetric traversable wormholes (Einstein–Rosen bridges) within the framework of Ken-ji Hamada's renormalizable and background-free quantum gravity. Using the conformal-mode decomposition g_ = e^2g_, the Riegert and Weyl sectors of the effective action, the running coupling t (r), and the dynamical factor B (r), we derive the complete set of field equations in Morris–Thorne form. The system reduces to two independent fourth-order ODEs for the combinations f = 2 + and g = - of the metric potentials. We solve these analytically in the linearized regime, reconstruct the full metric, apply boundary conditions (regularity at the throat, asymptotic flatness, smoothness), and derive the traversability conditions including the null energy condition (NEC) violation. Numerical estimates show that macroscopic wormholes (r₀ = 1 m) require exotic matter of order the Jupiter mass, with quantum corrections suppressed by factors of O (10^-70) ; Planck-scale wormholes (r₀ _) are formally possible but not useful for macroscopic travel. The role of ghost modes and BRST conformal invariance in ensuring unitarity is discussed. We conclude that Hamada's theory permits traversable wormhole solutions, but macroscopic traversability demands exotic matter quantities comparable to classical general relativity, as quantum gravitational corrections are negligible at macroscopic scales.
Yuriy N. Berdinsky (Thu,) studied this question.