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.

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

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

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