Langlands Program from TGD Point of View

Abstract

Langlands correspondence is for mathematics what unified theories are for physics. The number theoretic vision about TGD has intriguing resemblances with number theoretic Langlands program. There is also geometric variant of Langlands program. In this article, I will try to relate the general ideas of Langlands program to those behind TGD. Physics as geometry of WCW ("world of classical worlds") and physics as generalized number theory are the two visions about quantum TGD: This division brings in mind geometric and number theoretic Langlands programs. This motivates reconsideration of Langlands program from TGD point of view. I have written about this subject but TGD has evolved considerably since then so that it is time for a second attempt to understand what Langlands is about.