**Subject:** Fwd: Torsion and Connection

**Date:** Wed, 25 Mar 2009 11:05:15 EDT

Definitively, this is an important difference, the Christoffel symbols are not tensorial, while torsion is and the association with spin is possible.

2009/3/25

> It may be objected that the connection is not a tensor whereas the > angular energy momentum density is a tensor, so one cannot be proportional > to the other. The answer is that the torsion is a tensor because it is the > antisymmetric difference of two connections and so torsion can be > proportional to angular energy / momentum density. Using the antisymmetry of > the connection torsion may be written formally as twice the connection. The > connection does not transform as a tensor, but the antisymmetric difference > of two connections transforms as a tensor, the torsion tensor. The reason is > that the inhomogeneous terms in the coordinate transformations of the two > connections cancel out. This is shown in detail by Carroll, chapters one to > three. > > > > > > >

Agreed with Diego Rapoport, just sent over the proof with complete details.

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