Physics Formulae/Particle 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

Conservation of Lepton Number
Conservation of Baryon Number
Conservation of Strangeness
Eightfold Way
Weak Force

Strong Force	$\begin{matrix} ℒ_{Q C D} & = {\bar{ψ}}_{i} (i γ^{μ} (D_{μ})_{i j} - m δ_{i j}) ψ_{j} - \frac{1}{4} G_{μ ν}^{a} G_{a}^{μ ν} \\ = {\bar{ψ}}_{i} (i γ^{μ} \partial_{μ} - m) ψ_{i} - g G_{μ}^{a} {\bar{ψ}}_{i} γ^{μ} T_{i j}^{a} ψ_{j} - \frac{1}{4} G_{μ ν}^{a} G_{a}^{μ ν}, \end{matrix}$
Noether's Theorem
Electroweak Interaction	: $ℒ_{E W} = ℒ_{g} + ℒ_{f} + ℒ_{h} + ℒ_{y} .$ $ℒ_{g} = - \frac{1}{4} W_{a}^{μ ν} W_{μ ν}^{a} - \frac{1}{4} B^{μ ν} B_{μ ν}$ $ℒ_{f} = {\overline{Q}}_{i} i D / Q_{i} + {\overline{u}}_{i}^{c} i D / u_{i}^{c} + {\overline{d}}_{i}^{c} i D / d_{i}^{c} + {\overline{L}}_{i} i D / L_{i} + {\overline{e}}_{i}^{c} i D / e_{i}^{c}$ $ℒ_{h} = \| D_{μ} h \|^{2} - λ {(\| h \|^{2} - \frac{v^{2}}{2})}^{2}$ $ℒ_{y} = - y_{u i j} ϵ^{a b} h_{b}^{†} {\overline{Q}}_{i a} u_{j}^{c} - y_{d i j} h {\overline{Q}}_{i} d_{j}^{c} - y_{e i j} h {\overline{L}}_{i} e_{j}^{c} + h . c .$
Quantum Electrodynamics	: $ℒ = \bar{ψ} (i γ^{μ} D_{μ} - m) ψ - \frac{1}{4} F_{μ ν} F^{μ ν},$