From Scalar Sheets to Mass Volume: Redefining Field Permeation via Closed Surface Integration

This paper reinterprets the concept of scalar field permeation, commonly used in the Higgs mechanism, through the lens of closed surface theory. Instead of assuming scalar values exist uniformly throughout space, we propose that scalar values are distributed across equipotential surfaces—like sheets bearing patterned density—and that real-space volume and mass emerge through the geometric stacking and integration of these surfaces. Mass is defined as the total scalar integration over these closed surfaces, while density corresponds to the concentration of stable, resonant surfaces (e.g., molecular structures) per unit volume. This geometric framework offers an intuitive and unified reinterpretation of scalar fields, volume, and mass, resolving ambiguities in conventional field theories by anchoring them in topological structure. Author: Tetsuo Konno(今野哲夫) https://orcid.org/0009-0002-1842-7865