280 research outputs found
Inner fluctuations of the spectral action
We prove in the general framework of noncommutative geometry that the inner
fluctuations of the spectral action can be computed as residues and give
exactly the counterterms for the Feynman graphs with fermionic internal lines.
We show that for geometries of dimension less or equal to four the obtained
terms add up to a sum of a Yang-Mills action with a Chern-Simons action.Comment: 18 pages, 4 figures Equation 1.6 correcte
The Witt construction in characteristic one and Quantization
We develop the analogue of the Witt construction in characteristic one. We
construct a functor from pairs of a perfect semi-ring of characteristic one and
an element strictly larger than one, to real Banach algebras. We find that the
entropy function familiar in thermodynamics, ergodic theory and information
theory occurs uniquely as the analogue of the Teichmuller polynomials in
characteristic one. We then apply the construction to the semi-field of
positive real numbers with max as addition, 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
of the field of real numbers relevant both in number theory and quantum
physics.Comment: Dedicated to Henri Moscovic
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