The transition functions are derivable from the principle bundle connections: . Gives

Let covariant derivative on on a local section.

. This could be written as: if the is understood.

Then . Also,

For quarks, use SU(3) principle bundle. Quarks have a 3-d representation. Then is the dirac equation with . Physicists often insert i's to make A hermitian and put in scaling factors.

source

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