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math.NT2004★ 14 cited
Renormalization and motivic Galois theory
Alain Connes, Matilde Marcolli
We investigate the nature of divergences in quantum field theory, showing that they are organized in the structure of a certain `` motivic Galois group'', which is uniquely determi…
math.NT2004★ 46 cited
From Physics to Number Theory via Noncommutative Geometry. Part I: Quantum Statistical Mechanics of Q-lattices
Alain Connes, Matilde Marcolli
This is the first installment of a paper in three parts, where we use noncommutative geometry to study the space of commensurability classes of Q-lattices and we show that the arit…