Matrix Gauge Fields and Noether's theorem

TL;DR

This paper explores the foundational aspects of gauge fields and conservation laws in physics, focusing on elementary variational principles and matrix-valued functions without delving into advanced mathematics.

Contribution

It provides a simplified, elementary perspective on gauge fields and Noether's theorem, avoiding complex functional analysis or differential geometry.

Findings

Clarifies the role of matrix-valued functions in gauge theories

Connects variational principles with conservation laws

Offers insights into pre-quantized wave equations

Abstract

These notes have been triggered by physicist's considerations on (1)'Pre-quantized wave equations' for matter fields, (2) Conservation laws, (3) Gauge Field extensions. All starting from variational principles. These notes do not contain functional analysis or differential geometry. Only bare elementary considerations on matrix-valued functions. As a motivation there is a lengthy preface/summary.