Quantum Behavior in Asymmetric, Weyl-Like Cartan Geometries

TL;DR

This paper explores a Weyl-like Cartan geometry model that reproduces Schr"odinger field behavior from a purely geometric action, revealing subtle general relativistic effects and potential new mechanisms for mass and spin phenomena.

Contribution

It introduces a geometric framework that naturally derives Schr"odinger dynamics and suggests novel spin and mass mechanisms within a gauge-invariant setting.

Findings

Most differences from conventional Schr"odinger theory are unobservable in flat spacetime.

The wavefunction's conjugate is not always the exact complex conjugate of the primary.

The model hints at spin-like phenomena and new mass generation mechanisms.

Abstract

This discussion examines recent developments in the theory of a Weyl-like, Cartan geometry with natural Schr\"odinger field behavior proposed previously. In that model, very nearly exactly a coupled Einstein-Maxwell- Schr\"odinger, classical field theory emerges from a gauge invariant, purely geometric action based solely on variations of the electromagnetic potentials and the metric. In spite of this, only slight differences appear between the resulting Schr\"odinger part, and the conventional theory of the Schr\"odinger field. Close examination of the differences reveals that most are general relativistic effects which are unobservable in flat spacetime, and which are estimated to interact significantly only via their gravitational fields, or on scales comparable with neutrino interaction cross sections. The only remaining difference is that the wavefunction obeying the conjugate wave equation is not always restricted to be exactly the complex conjugate of the primary wavefunction. Generalizations of the model lead naturally to spinlike phenomena, a possible new mechanism for a theory of rest mass, and spinor connections containing the form of an SU(2) potential.