More about Physical Interpretation of Algebraic Extensions of Rationals

Abstract

In this article a more detailed view about emergence of preferred p-adic primes as ramified primes is discussed. All boils down to quantum criticality. Classically it corresponds to appearance of space-time surface whose ends at the boundaries of CD collapse to single 3-surface (or partonic 2-surface) to give singular covering. In the parameter space characterized by the algebraic extension of rational criticality corresponds to a prime ideal corresponding to ramified prime - ramification is indeed analogous to criticality. For other than ramified primes this collapse does not occur and the sheets define separate 3-surfaces related to each other by Galois group serving as a number theoretical symmetry group- the connection with the Langlands program is obvious. The remaining discrete degrees are however physical for ramified space-time surfaces although the action of Galois group is trivial.