Classical and Quantum Theory with a New Symmetry

TL;DR

This paper introduces a new symmetry between coordinates and momenta to develop classical and quantum particle theories coupled with gauge fields, revealing implications for field dynamics, space-time geometry, and quantum measurement.

Contribution

It proposes a formal symmetry that necessitates dynamic gauge fields and non-flat space-time, offering a novel approach to quantum theory without the measurement problem.

Findings

Field must have dynamic degrees of freedom

Space-time must be non-flat

Quantum theory is free of the measurement problem

Abstract

A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic degrees of freedom and to be a connection in a non-flat space-time manifold, and (b) leads to a quantum theory free of the measurement problem. It is speculated that gravitomagnetism could be a possible source of the gauge field.