Conformal structure of quantum wave mechanics

Abstract

This work interprets the quantum terms in a Lagrangian, and consequently of the wave equation and momentum tensor, in terms of a modified spacetime metric. Part I interprets the quantum terms in the Lagrangian of a Klein–Gordon field as scalar curvature of conformal dilation covector nm that is proportional to [Formula: see text] times the gradient of wave amplitude R. Part II replaces conformal dilation with a conformal factor [Formula: see text] that defines a modified spacetime metric [Formula: see text]= exp[Formula: see text], where g is the gravitational metric. Quantum terms appear only in metric [Formula: see text] and its metric connection coefficients. Metric [Formula: see text] preserves lengths and angles in classical physics and in the domain of the quantum field itself. [Formula: see text] combines concepts of quantum theory and spacetime geometry in one structure. The conformal factor can be interpreted as the limit of a distribution of inclusions and voids in a lattice that cause the metric to bulge or contract. All components of all free quantum fields satisfy the Klein–Gordon equation, so this interpretation extends to all quantum fields. Measurement operations, and elements of quantum field theory are not considered.