Physics Formulae/Particle Physics Formulae

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of particle physics.

Atoms and Nuclei

Fermi Energy	$E_{F}=(3/16{\sqrt {2}}\pi )^{2/3}h^{2}n^{2/3}m\,\!$
Mass Number	$A=Z+N\,\!$
Nuclear Radius	$r=r_{0}A^{1/3},r_{0}\approx 1.2fm\,\!$
Mass Excess	$\Delta =M-A\,\!$
Radioactive Decay	$N=N_{0}e^{-\lambda t}\,\!$
Hubble Constant	$H=71.0km/s\,\!$
Hubble's Law	$v=Hr\,\!$

Quantum Numbers of Quark Flavuors

Conservation of Lepton Number	$\,\!$
Conservation of Baryon Number	$\,\!$
Conservation of Strangeness	$\,\!$
Eightfold Way	$\,\!$
Weak Force	$\,\!$

The Fundamental Forces

Strong Force	${\begin{aligned}{\mathcal {L}}_{\mathrm {QCD} }&={\bar {\psi }}_{i}\left(i\gamma ^{\mu }(D_{\mu })_{ij}-m\,\delta _{ij}\right)\psi _{j}-{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu }\\&={\bar {\psi }}_{i}(i\gamma ^{\mu }\partial _{\mu }-m)\psi _{i}-gG_{\mu }^{a}{\bar {\psi }}_{i}\gamma ^{\mu }T_{ij}^{a}\psi _{j}-{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu }\,,\\\end{aligned}}\,\!$
Noether's Theorem	$\,\!$
Electroweak Interaction	:${\mathcal {L}}_{EW}={\mathcal {L}}_{g}+{\mathcal {L}}_{f}+{\mathcal {L}}_{h}+{\mathcal {L}}_{y}.\,\!$ ${\mathcal {L}}_{g}=-{\frac {1}{4}}W_{a}^{\mu \nu }W_{\mu \nu }^{a}-{\frac {1}{4}}B^{\mu \nu }B_{\mu \nu }\,\!$ ${\mathcal {L}}_{f}={\overline {Q}}_{i}iD\!\!\!\!/\;Q_{i}+{\overline {u}}_{i}^{c}iD\!\!\!\!/\;u_{i}^{c}+{\overline {d}}_{i}^{c}iD\!\!\!\!/\;d_{i}^{c}+{\overline {L}}_{i}iD\!\!\!\!/\;L_{i}+{\overline {e}}_{i}^{c}iD\!\!\!\!/\;e_{i}^{c}\,\!$ ${\mathcal {L}}_{h}=|D_{\mu }h|^{2}-\lambda \left(|h|^{2}-{\frac {v^{2}}{2}}\right)^{2}\,\!$ ${\mathcal {L}}_{y}=-y_{u\,ij}\epsilon ^{ab}\,h_{b}^{\dagger }\,{\overline {Q}}_{ia}u_{j}^{c}-y_{d\,ij}\,h\,{\overline {Q}}_{i}d_{j}^{c}-y_{e\,ij}\,h\,{\overline {L}}_{i}e_{j}^{c}+h.c.\,\!$
Quantum Electrodynamics	:${\mathcal {L}}={\bar {\psi }}(i\gamma ^{\mu }D_{\mu }-m)\psi -{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }\;,\,\!$