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 P: n/a Jay R. Yablon: > For an Abelian Field strength F_uv, one can write the two-form, in polar > coordinates, as: > > F = F_uv dx^u dx^v = - (g/4pi) sin theta d-theta d-phi (1) > > For a non-Abelian field strength F_i_uv where i is the index of the Yang > Mills group being considered, and T^i are the group generators, we have > (using SU(2) as an example): > > F = T^i F_i = T^i F_i_uv dx^u dx^v > > / F_3_uv F_1_uv + iF_2_uv \ > = | | dx_u dx_v (2) > \ F_1_uv - iF_2_uv -F_3_uv / > > Thus, F is no longer a simple scalar like - (g/4pi) sin theta d-theta > d-phi, but it is a two-by-two matrix transforming under SU(2). > > I may figure it our by the time someone replies, but how would one form > (2) with explicit polar coordinates, analogously to (1)? First note that (1) isn't correct, it should read: F = F_uv dx^u dx^v = - F_theta_phi (g/4pi) sin theta d^theta d^phi (1) Then it isn't that difficult. You can write the F_i_uv dx^u dx^nu like in (1), and put them in the matrix (distributing dx^u dx^nu in the matrix.) Then -(g/4pi) sin theta d^theta d^phi factorize and get out of the matrix. GML