The Lagrangian equation...
I request to initiate a thread on what I only know as the Lagrangian equation. The original published scientific paper derivation proof is unknown to me.
[math]\;[/math] Lagrangian equation:
[math]\mathcal{L} = \underbrace{\mathbb{R}}_{GR} - \overbrace{\underbrace{\frac{1}{4} F_{\mu \nu} F^{\mu \nu}}_{Yang-Mills}}^{Maxwell} + \underbrace{i \overline{\psi} \gamma^\mu D_\mu \psi}_{Dirac} + \underbrace{|D_\mu h|^2-V\left(|h| \right)}_{Higgs} + \underbrace{h \overline{\psi} \psi}_{Yukawa} = 0[/m
Electroweak Langrangian
L=−14WαμνWμνα−14BμνBμν+Ψ¯¯¯¯iγμDμΨ
W1,2,3μ
and Bμ
Covariant Derivative
Dμ=∂μ+igWμτ2−ig´2Bμ
mass eigenstates observed in experiments are linear combinations of the electroweak eigenstates. Hence W− and W+
W±μ=12−−√(W1μW2μ)
γ
and Z are\
Aμ=BmucosθW+W3μsinθW
Zμ=BmusinθW+W3μcosθW
Cabibbo-Kobayashi-Maskawa matrix
⎛⎝⎜⎜d´s´b´⎞⎠⎟⎟⎛⎝⎜VudVcdVtdVusVcsVtsVubVcbVtb⎞⎠⎟⎛⎝⎜dsb⎞⎠⎟
symmtric massles