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Tensor calculus (tensor analysis) is a systematic extension of vector calculus to multivector and tensor fields in a form that is independent of the choice of coordinates on the relevant manifold, but which accounts for respective sub-spaces, their symmetries, and their connections.

8 votes
1 answer
198 views

Minimal spin connection, and the standard content of GR

In Sec. 12.1 of 'Superstring Theory', by Green, Schwarz, and Witten, the minimal spin connection is motivated as follows: If we are to avoid modifying the standard content of general relativity, …
John Fredsted's user avatar
4 votes
1 answer
405 views

Decomposition of the torsion tensor

See Update below. Consider the torsion tensor $T_{\mu\nu\rho} = -T_{\mu\rho\nu}$. In a local Lorentz frame, as determined by a vierbein $e^{a}{}_{\mu}$, it may equivalently be given as $T_{abc} = e^{ …
John Fredsted's user avatar