A Yang-Mills gauge field is a lie algebra valued one-form

tex2html_wrap125 in tex2html_wrap126 , tex2html_wrap127 , tex2html_wrap128 , tex2html_wrap129

Thes connections can be used to define a horizontal life of a curve.

tex2html_wrap130 . This is a first order differential equation. tex2html_wrap131 .

tex2html_wrap132 tex2html_wrap133

tex2html_wrap134 where tex2html_wrap135 are the canonical basis and tex2html_wrap136 is the covariant derivative.

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