Alpha Institute for Advanced Studies

(AB)C = A(BC)

(G. Stephenson, “Mathematical Methods of Science Students”, (Longmans 1968), p. 287, eq. (18)). Will think about the second point and report back.

In a message dated 29/10/2012 19:05:05 GMT Standard Time, writes:

Eq.(16) seems to be problematic because mu in eq.(15) is a dummy index, q sup a sub mu can not be isolated by multiplying with another g sub mu,nu.
In eq.(43) R can only be defined in this way because the tensors Omega and q are linearly dependent. This works in the example of the circular complex basis, I am not sure if this works in cases where the vector spaces or bases significantly differ. Perhaps one has to start with the wave equation ( 46) directly in that case.

Horst

Am 29.10.2012 11:37, schrieb EMyrone

This note gives the foundations of a new type of differential geometry in which the tetrad is defined as a mixed index metric. The whole of Cartan’s differential geometry can be developed in terms of mixed index metric, and classical and quantum equations of ECE unified physics derived. These contain more information because they are equations of a higher topology. This is the first note in this series.