The Witt construction in characteristic one and quantization
Alain Connes · Contemporary mathematics - American Mathematical Society · 2011
Dedicated to Henri Moscovici, with admiration and friendship Abstract. We develop the analogue of the Witt construction in characteristic one. We construct a functor from pairs (R,ρ) of a perfect semi-ring R of characteristic one and an element ρ> 1 of R to real Banach algebras. We find that the entropy function occurs uniquely as the analogue of the Teichmüller polynomials in characteristic one. We then apply the construction to the semi-field Rmax + which plays a central role in idempotent analysis and tropical geometry. Our construction gives the inverse process of the “dequantization” and provides a first hint towards an extension Run of the field of real numbers relevant both in number theory and quantum physics. 1. Foreword ThecelebrationofHenri’s65thbirthdaygivesmealongawaitedoccasiontoexpress mydeep gratitudeto him, for hisindefectible friendship in ourlongjourneythrough mathematics, since the first time we met in Princeton in the fall of 1978. Besides the great enlightening moments, those that I cherish most are the times when we