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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Covariant derivative in Standard Model

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**