Volume-Preserving Diffeomorphisms' versus Local Gauge Symmetry

TL;DR

This paper introduces a novel quantum electrodynamics framework where photons are composite scalars, replacing local gauge symmetry with an infinite-dimensional global symmetry, leading to new solutions and effects beyond traditional Maxwell theory.

Contribution

It proposes a new QED model based on volume-preserving diffeomorphisms, replacing gauge symmetry with a global symmetry, and explores its implications for electromagnetic solutions.

Findings

Solutions of Maxwell's equations are included in the new system.

The new theory exhibits additional non-Maxwell solutions with unique effects.

It predicts gauge-invariant photon mass generation with arbitrary mass.

Abstract

We present a new form of Quantum Electrodynamics where the photons are composites made out of zero-dimensional scalar ``primitives''. The r\^{o}le of the local gauge symmetry is taken over by an {\em infinite-dimensional global Noether symmetry} -- the group of volume-preserving (symplectic) diffeomorphisms of the target space of the scalar primitives. Similar construction is carried out for higher antisymmetric tensor gauge theories. Solutions of Maxwell's equations are automatically solutions of the new system. However, the latter possesses additional non-Maxwell solutions which display some interesting new effects: (a) a magneto-hydrodynamical analogy, (b) absence of electromagnetic self-energy for electron plane wave solutions, and (c) gauge invariant photon mass generation, where the generated mass is arbitrary.