# Noether's Theorem for a Fixed Region

## TL;DR

This paper presents an elementary proof of Noether's first Theorem emphasizing that global quasi-symmetry needs only to hold for a fixed region, and discusses conditions for gauging such symmetries.

## Contribution

It offers a simplified proof of Noether's Theorem highlighting the fixed region aspect and provides criteria for gauging global quasi-symmetries.

## Key findings

- Global quasi-symmetry suffices for Noether's Theorem when holding on one fixed region
- Conditions for gauging a global quasi-symmetry are established
- Elementary proof approach simplifies understanding of Noether's Theorem

## Abstract

We give an elementary proof of Noether's first Theorem while stressing the magical fact that the global quasi-symmetry only needs to hold for one fixed integration region. We provide sufficient conditions for gauging a global quasi-symmetry.