Quantum fields and motives Export

@article{citeulike:463976, abstract = {This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field theories share a common universal symmetry realized as a motivic Galois group, whose action is dictated by the divergences and generalizes that of the renormalization group. The existence of such a group was conjectured by P. Cartier based on number theoretic evidence and on the Connes-Kreimer theory of perturbative renormalization. The group provides a universal formula for counterterms and is obtained via a Riemann-Hilbert correspondence classifying equivalence classes of flat equisingular bundles, where the equisingularity condition corresponds to the independence of the counterterms on the mass scale.}, archivePrefix = {arXiv}, author = {Connes, Alain and Marcolli, Matilde}, citeulike-article-id = {463976}, citeulike-linkout-0 = {http://arxiv.org/abs/hep-th/0504085}, citeulike-linkout-1 = {http://arxiv.org/pdf/hep-th/0504085}, eprint = {hep-th/0504085}, keywords = {differential, galoisgroup, geometry, noncommutative, numbertheory, physics, renormalization}, month = {Apr}, posted-at = {2006-01-13 06:44:56}, priority = {2}, title = {Quantum fields and motives}, url = {http://arxiv.org/abs/hep-th/0504085}, year = {2005} }

TY - JOUR ID - citeulike:463976 L3 - citeulike-article-id:463976 N2 - This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field theories share a common universal symmetry realized as a motivic Galois group, whose action is dictated by the divergences and generalizes that of the renormalization group. The existence of such a group was conjectured by P. Cartier based on number theoretic evidence and on the Connes-Kreimer theory of perturbative renormalization. The group provides a universal formula for counterterms and is obtained via a Riemann-Hilbert correspondence classifying equivalence classes of flat equisingular bundles, where the equisingularity condition corresponds to the independence of the counterterms on the mass scale. TI - Quantum fields and motives KW - differential KW - galoisgroup KW - geometry KW - noncommutative KW - numbertheory KW - physics KW - renormalization AU - Connes, Alain AU - Marcolli, Matilde PY - 2005/Apr/09/ UR - http://arxiv.org/abs/hep-th/0504085 ER -