The covariant derivative in standard model is given by(adsbygoogle = window.adsbygoogle || []).push({});

D^{μ}= ∂^{μ}+ ig_{s}G_{a}^{μ}L_{a}+ ig W_{b}^{μ}T_{b}+ ig'B^{μ}Y

where G_{a}^{μ}are the eight gluon fields, W_{b}^{μ}the three weak interaction bosons and B^{μ}the single hypercharge boson. The L_{a}'s are SU(3)_{C}generators (the 3×3 Gell-Mann matrices ½ λ_{a}for triplets, 0 for singlets), the T_{b}'s are the SU(2)_{L}generators (the 2×2 Pauli matrices ½ τ_{b}for doublets, 0 for singlets), and the Y's are the U(1)_{Y}charges.

It looks like the second term is a 3×3 matrix, the third term is a 2×2 matrix, and the last term is a single term. How can they add up? Is D^{μ}a 3×3 matrix or something else?

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# A Covariant derivative in Standard Model

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