Skip to main content\(\addtolength{\jot}{0.5ex}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\bivec}[1]{\overset{\curvearrowleft}{#1}}
\newcommand{\proofmark}{\class{twemoji-proofmark}{\text{M}}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Section 1.4 Global vs. Local (Gauge) Symmetry
202608010001 |
global symmetry local (gauge) symmetry Noether's theorem variations generators
Table 1.4.1. Global vs. Local (Gauge) Symmetry
| Symmetry range |
|
Different shift at every point
|
| Generator action |
Translates states through space and time
|
Rotates internal phases locally
|
| Variational result |
Yields a conserved quantity (e.g., momentum and energy)
|
Yields a physical force field (e.g., electromagnetism and gluons)
|