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Tex fixed, g-1 replaced by the inverse
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edit approved Jun 11, 2014 at 18:27
ThiKu
edit approved Jun 11, 2014 at 18:27
ThiKu
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You should check out ThedoreTheodore Frankel's Geometry of Physics. There is a section on the gauge group . The cartan three form is the three form from the Chern Simons term at a flat connection  . A flat connection is when the potential A is equal to the g-1^dg $g^{-1}dg$. In the chern simonsChern Simons 3 form you have A^A^A. At pure gauge this becomes tr(g-1^dg^g-1^dg^g-1^dg)$Tr(g^{-1}dg\wedge g^{-1}dg\wedge g^{-1}dg)$. This term is proportional to the cartan 3 form. I hope this helped.

You should check out Thedore Frankel's Geometry of Physics. There is a section on the gauge group . The cartan three form is the three form from the Chern Simons term at a flat connection  . A flat connection is when the potential A is equal to the g-1^dg . In the chern simons 3 form you have A^A^A. At pure gauge this becomes tr(g-1^dg^g-1^dg^g-1^dg). This term is proportional to the cartan 3 form. I hope this helped.

You should check out Theodore Frankel's Geometry of Physics. There is a section on the gauge group . The cartan three form is the three form from the Chern Simons term at a flat connection. A flat connection is when the potential A is equal to the $g^{-1}dg$. In the Chern Simons 3 form you have A^A^A. At pure gauge this becomes $Tr(g^{-1}dg\wedge g^{-1}dg\wedge g^{-1}dg)$. This term is proportional to the cartan 3 form. I hope this helped.

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user50728
user50728

You should check out Thedore Frankel's Geometry of Physics. There is a section on the gauge group . The cartan three form is the three form from the Chern Simons term at a flat connection . A flat connection is when the potential A is equal to the g-1^dg . In the chern simons 3 form you have A^A^A. At pure gauge this becomes tr(g-1^dg^g-1^dg^g-1^dg). This term is proportional to the cartan 3 form. I hope this helped.