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)?

Thanks,

Jay.

_____________________________

Jay R. Yablon

Email:

jyablon@nycap.rr.com
Web site:

http://home.nycap.rr.com/jry/FermionMass.htm
sci.physics.foundations co-moderator