# 8: Symmetries of the theory of strong interactions

- Page ID
- 15051

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

The first time people realized the key role of symmetries was in the plethora of particles discovered using the first accelerators. Many of those were composite particle (to be explained later) bound by the strong interaction.

- 8.4: SU(4), SU(5), and SU(6) flavor symmetries
- Once we have three flavors of quarks, we can ask the question whether more flavors exists. At the moment we know of three generations of quarks, corresponding to three generations (pairs).

- 8.5: Color Symmetry
- We assume that quarks come in three colours. This naturally leads to yet another SU(3) symmetry, which is actually related to the gauge symmetry of strong interactions, QCD.

Thumbnail: Chromodynamic fields due to color charges, these are the neutral/"colorless" combinations. (Public Domain; Maschen).