# Weinberg-Salam 模型

Weinberg-Salam 模型Steven WeinbergAbdus Salam提出嘅弱電統一規範場論模型。

${\displaystyle {\mathcal {L}}=-(1/4)A_{\mu \nu }A^{\mu \nu }-(1/4)B_{\mu \nu }B^{\mu \nu }}$ ${\displaystyle +\left[{\bar {R}}_{e}(i\partial \!\!\!/-g'b\!\!\!/)R_{e}+{\bar {L}}_{e}(i\partial \!\!\!/-{\frac {g'}{2}}B\!\!\!/+G{\frac {\tau _{i}}{2}}A\!\!\!/_{i})L_{e}-G_{e}({\bar {L}}_{e}R_{e}\phi +\phi ^{\dagger }{\bar {R}}_{e}L_{e})+(e\leftrightarrow \mu )\right]}$ ${\displaystyle +\left(\partial _{\mu }\phi -i{\frac {g'}{2}}B_{\mu }\phi -{\frac {ig}{2}}\tau ^{i}A_{\mu i}\phi \right)^{\dagger }\left(\partial ^{\mu }\phi -i{\frac {g'}{2}}B^{\mu }\phi -{\frac {ig}{2}}\tau ^{i}A_{i}^{\mu }\phi \right)-V(\phi ^{\dagger }\phi )}$

• ${\displaystyle A_{\mu \nu }:=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }+gA_{\mu }\times A_{\nu }}$SU(2) 規範場 ${\displaystyle A_{\mu }}$嘅力
• ${\displaystyle B_{\mu \nu }:=\partial _{\mu }B_{\nu }-\partial _{\nu }B_{\mu }}$係U(1)場（電磁場${\displaystyle B_{\mu }}$嘅力
• g 係荷
• ${\displaystyle \partial \!\!\!/}$係Dirac算子(en:Dirac operator)，用費曼符號(en:Feynman slash notation)寫
• g'/2 係U(1)藕合常數(? en:coupling constant)
• ${\displaystyle L_{e}={\begin{pmatrix}\nu _{e}\\e_{L}\end{pmatrix}}}$電子中微子電子嘅左 helicity (en:helicity (partical physics))
• ${\displaystyle L_{\mu }:={\begin{pmatrix}\nu _{\mu }\\\nu _{L}\end{pmatrix}}}$ 係 muon中微子同 muon 嘅左helicity
• ${\displaystyle \phi :={\begin{pmatrix}\phi ^{\dagger }\\\phi _{0}\end{pmatrix}}}$ 係複純量嘅兩元組
• ${\displaystyle V:=\mu ^{2}\phi ^{\dagger }\phi +\lambda (\phi ^{\dagger }\phi )^{2}}$係勢

## 註

1. Itzykson / Zuber, p.621