Talk:Spin connection

Final form of spin connection
In the end of derivation of spin connection by the tetrad postulate, the final form consisting of 2 tetrads was acquired by using some differentiation identities of contracted tetrads. The second step, where 4 tetrads become 2, does not seem to be correct. Applying differentiation by parts results into one term containing derivative of a product of two tetrads with no contraction, and the other term you have but with a minus. Is it your personal derivation or it has been proved somewhere else? — Preceding unsigned comment added by 83.85.144.163 (talk) 19:53, 25 March 2015 (UTC)

error in final form of spin connection
I think the mistake is in the final step. Two tetrads contract to give a metric tensor, and this has been used to lower the index on the tetrad being differentiated. This is incorrect since the partial derivative of the metric tensor is generally nonzero. The same problem makes the second equation in the derivation (with the spin connection alone on the left hand side) incorrect as well. — Preceding unsigned comment added by 128.111.9.41 (talk) 00:40, 26 March 2015 (UTC)

Wrong factor
In the formula for spin coefficient 1/2 should not be there. Is is true that a linear combination of 3 antisymmetrized tetrad postulate equations eventually we are left with with one spin connection with a factor 2, but antisymmetrisation comes with a factor of 1/2, hence no numerical factor, apart from 1, should be present. — Preceding unsigned comment added by 83.85.144.163 (talk) 21:53, 2 July 2015 (UTC)

Which is it?
The first paragraph of the article says:


 * In differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle. It is induced, in a canonical manner, from the affine connection.

The second says:


 * The spin connection occurs in two common forms: the Levi-Civita spin connection, when it is derived from the Levi-Civita connection, and the affine spin connection, when it is obtained from the affine connection.

So at first the article flatly claims the spin connection is induced from the affine connection, and then it says there are two forms and that's just one. This inconsistency should be fixed.