Geometrical structure and nature of cylindrical space associated with point particles

A unific helical field as geometric structure in a cylindrical space is proposed which is capable of determining attributes inherent to point-like particles. An operational discussion on transition between our observational space and the warped infinitesimal space is expanded. It is seen that the rotational eigenvalue equation, which is satisfied by vector field equivalent to a Gromeka-Beltrami flow subject to fluid and plasma physics, provides a spatio-unifier that sustains complex orthogonal coupling between a rotational, internal coordinate space and angular momentum space. Self-consistent normalization of the rotational coordinate owing to the unifier is shown to be responsible for the renormalization in quantum electrodynamics (QED). For the demonstration, a numerical value corresponding to the fine-structure constant is derived from theoretical analysis involving the rotational eigenvalue that charged leptons should refer to. It is found that the eigenstates of the fields having helical mirror-asymmetry are reflected in parity violation in beta-decay, and also, the chiral eigenstates of the lowest order even mode exhibit affinity for gravitational interaction. This study is essential for going beyond the standard model and elucidating origin of space-time.