English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

One way of describing gauge theories in physics is to assign a vector space$V_{x}$ to each space time point $x.$ For each $x$ the field $\psi$ takesvalues $\psi(x)$ in $V_{x}.$ The freedom to choose a basis in each $V_{x}$introduces gauge group operators and their Lie algebra representations todefine parallel transformations between vector spaces. This paper is anexploration of the extension of these ideas to include the underlying scalarcomplex number fields. Here a Hilbert space, $\bar{H}_{x},$ as an example of$V_{x},$ and a complex number field, $C_{x},$ are associated with each spacetime point. The freedom to choose a basis in $H_{x}$ is expanded to include thefreedom to choose complex number fields. This expansion is based on thediscovery that there exist representations of complex (and other) numbersystems that differ by arbitrary scale factors. Compensating changes must bemade in the basic field operations so that the relevant axioms are satisfied.This results in the presence of a new real valued gauge field $\vec{A}(x).$Inclusion of $\vec{A}(x)$ into covariant derivatives in Lagrangians results inthe description of $\vec{A}(x)$ as a gauge boson that can have mass. The greataccuracy of QED suggests that the coupling constant of $\vec{A}(x)$ to matterfields is very small compared to the fine structure constant. Other physicalproperties of $\vec{A}(x)$ are not known at present.

New Gauge Field from Extension of Space Time Parallel Transport of Vector Spaces to the Underlying Number Systems