An Intrinsic Transport Theorem

During the summer of 1968 I invited John Pierce ( one of my best graduate students) out to visit me at Los Alamos, New Mexico. I wanted to show him around the lab, and to do some work on differential forms. I conjectured that the theory of forms ought to be able to express transport theorems in an intrinsic (coordinate free) manner. During the day, John worked on the problem while I worked at LASL. When I came home in the evening we would try to come up with some cooperative results. Then, one Friday when I returned from the lab, I found that he had left me some notes on the kitchen table, saying that he had given up on the idea, and was going to Albuquerque to meet a friend for the weekend.

I stared at his notes and his conclusion in despair, but then as often happens with me, in a flash I had solved the problem. The important idea was the birth of the topological 3-form A^H, representing the intersection of the 1-form of Action and the 2 form of excitations.

I now call this 3-form Topological Spin, and use the notation A^G instead of A^H. The discovery of the period integrals of A^G then led to other 3-forms, in particular that 3-form A^F which I call Topological Torsion.

It is now apparent that these concepts have fundamental utility in understanding irreversible phenomena, as well as in the understanding of chirality and helicity in enantiomers. There are many articles and ideas on this web site that had their origin with this early article published in the Physics of Fluids Vol 12, Number 9, (1969) p1941-1943.

Back in those days almost no one in the applied physics world knew anything about differential forms, much less, about topology.


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