An extremely useful relation between the Kronecker delta and the Levi-Civita symbol.
The brackets mean that we completely anti-symmetrize in the indices m,npic.twitter.com/Hp8tK8qZ3D
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This soldering of the frame bundle to spacetime has a thousand profound ramifications, none of which can be naturally accommodated into the normal framework of gauge theory. And it doesn't help to replace the frame bundle by its double-cover, the spin bundle. It too is soldered.
Yep, It doesn't help much indeed.: to replace the frame bundle and its double cover spin bundle. (Like simply connected Spin(n) and O(n,R)) and the Clifford Algebras and also: SL(2,C) and SO(3,1).
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