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Old 2007-06-04, 23:56   #2
m_f_h's Avatar
Feb 2007

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Originally Posted by Damian View Post
Can someone explain me in simple terms what is the covariant derivation?
For example if we take as a Manifold the unit circle in R^2, what would be its covariant derivation?
the explicit expr of the corvar deriv depends on the object : you have to add a term with the gauge potential (connection) for each index.
e.g. for R_ab^cd
DR_ab^cd = dR_ab^cd+R_eb^cd phi_a^e +R_ae^cd phi_a^e +R_ab^ed phi_e^c+R_ab^ce phi_e^d

sorry I may have not 100% mainstream conventions ,
also that expression might simplify (to zero of course, but suppose R was sth else than d phi + phi phi),
i dont remember well : I did that in an earlier life...

Last fiddled with by m_f_h on 2007-06-04 at 23:57
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