The Structure of Free Gauge Fields over Minkowski Space

TL;DR

This paper explores the classical and quantum structures of free gauge fields over Minkowski space, revealing their state spaces, mass spectra, and potential relation to dark matter.

Contribution

It demonstrates that free gauge fields form pre-Hilbert spaces at the classical level and discusses their quantization, including massless and massive field manifestations.

Findings

Free gauge fields form pre-Hilbert spaces classically.

Some free gauge fields have a continuous mass spectrum with no gap.

Massless and massive fields are different manifestations of the same field.

Abstract

It is shown that the physical states of a source free gauge field form pre-Hilbert spaces already on the classical level. These spaces may be closed in such a way that the determining characteristics remain. One type of free fields has a continuous mass spectrum with no mass gap. One type is massless. Dark matter may consist of (otherwise) free gauge fields. Second quantisation of free gauge fields yield G{\aa}rding-Wightman fields identifying the massless and the massive fields as different manifestations of the same field.