New Gauge Fields from Extension of Parallel Transport of Vector Spaces to Underlying Scalar Fields

TL;DR

This paper extends gauge theories by assigning separate scalar fields to each spacetime point, introducing new gauge fields A(x) and B(x), with B(x) likely representing the photon, and explores their implications in covariant derivatives.

Contribution

It introduces a novel extension of gauge theories by associating distinct scalar fields to each point, leading to new gauge fields and potential insights into gauge bosons.

Findings

Introduction of two gauge fields, A(x) and B(x), from extended scalar field framework.

B(x) identified as a likely photon field, massless and with small coupling.

A(x) remains of unknown nature, with optional mass and very weak coupling.

Abstract

Gauge theories can be described by assigning a vector space V(x) to each space time point x. A common set of complex numbers, C, is usually assumed to be the set of scalars for all the V{x}. This is expanded here to assign a separate set of scalars, C{x}, to V{x} for each x. The freedom of choice of bases, expressed by the action of a gauge group operator on the V{x}, is expanded here to include the freedom of choice of complex scale factors, c_{y,x}, as elements of GL(1,C) that relate C{y} to C{x}. A gauge field representation of c_{y,x} gives two gauge fields, A(x) and iB(x). Inclusion of these fields in the covariant derivatives of Lagrangians results in A(x) appearing as a gauge boson for which mass is optional and B(x) as a massless gauge boson. B(x) appears to be the photon field. The nature of A(x) is not known at present. One does know that the coupling constant of A(x) to matter fields is very small compared to the fine structure constant.