A principle bundle, P(M,G) has an associated vector bundle, tex2html_wrap115 Where the tex2html_wrap116 is a vector space with tex2html_wrap117 = dimension of pth representation of the group.

The transition functions are derivable from the principle bundle connections: tex2html_wrap118 . Gives tex2html_wrap119

Let tex2html_wrap120 covariant derivative on tex2html_wrap115 on a local section.

tex2html_wrap122 . This could be written as: tex2html_wrap123 if the tex2html_wrap124 is understood.

Then tex2html_wrap125 . Also, tex2html_wrap126

For quarks, use SU(3) principle bundle. Quarks have a 3-d representation. Then tex2html_wrap127 is the dirac equation with tex2html_wrap128 . Physicists often insert i's to make A hermitian and put in scaling factors.


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