Is the Hodge dual suited to simplify calculations as in paper 439?

From Email exchange:


Doug introduced the Hodge dual to hide certain information and to obtain simpler expressions for curvature tensors.  I have to discuss this with him in detail. It has to do with the fact that the essential information in Cartan geometry is contained in the antisymmetric parts of the connection.
Referring to paper 439, you can compute the Hodge duals of all tensors but this is not necessary in the path from the tetrad to the force field tensors. The Hodge duals of the connections were computed in that paper. From the examples it is seen that they are not necessarily simpler than the original connections. Theoretically you could compute the dual torsion from the Lambda connections and then identify with the E, B fields in the dual representation of the F tensor.


Am 26.10.2020 um 18:13 schrieb Russell Davis:
Hi Horst,

I’m glad the blog is back up and operational. I also like Myron’s original blog format (template) that Sean was to implement; it’s provides a pleasant visual continuity with all the past blog posts.

Doug also sent me a draft copy of his new paper (which you refer to on your latest blog post), in which he develops Hodge dual simplifications that capture the information of the tensor formulations. Can Doug’s approach be used in relation to your paper 439 to establish an even more handable equation set pathway for calculating or analyzing the features of a particular physical system?


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