A More Detailed View on the TGD Counterpart of Langlands Correspondence

Abstract

In TGD, geometric and number theoretic visions of physics are complementary. This complementarity is analogous to momentum position duality of quantum theory and implied by the replacement of a point-like particle with 3-surface, whose Bohr orbit defines space-time surface. At a very abstract level this view is analogous to Langlands correspondence. The recent view of TGD involving an exact algebraic solution of field equations based on holography = holomorphy vision allows to formulate the analog Langlands correspondence in 4-D context rather precisely. This requires a generalization of the notion of Galois group from 2-D situation to 4-D situation: there are 2 generalizations and both are required.