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Jay R. Yablon
Apr17-07, 05:00 AM
P: n/a
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)?


Jay R. Yablon
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sci.physics.foundations co-moderator

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