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Combinatorics and physics : Mini-Workshop on Renormalization, December 15-16, 2006, Max Planck Institut für Mathematik, Bonn, Germany : Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany / / Kurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom, editors
| Combinatorics and physics : Mini-Workshop on Renormalization, December 15-16, 2006, Max Planck Institut für Mathematik, Bonn, Germany : Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany / / Kurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2011] |
| Descrizione fisica | 1 online resource (480 p.) |
| Disciplina | 530.14/3 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Renormalization group
Quantum field theory Numerical integration |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-8218-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""List of participants""; ""One-particle irreducibility with initial correlations""; ""Multiple zeta values and periods: From moduli spaces to Feynman integrals""; ""From quantum electrodynamics to posets of planar binary trees""; ""Sweedler's duals and Schutzenberger's calculus""; ""Primitive elements of the Hopf algebra of free quasi-symmetric functions""; ""A Renormalisation Group approach to Stochastic Loewner Evolutions""; ""On the causal gauge principle""; ""1. Introduction""; ""2. Overview of the CGI method""; ""3. The abelian model""; ""4. Three MVBs""
""5. The Weinberg�Salam model within CGI""""6. Discussion""; ""References""; ""Abstract integration, combinatorics of trees and differential equations""; ""Rooted trees appearing in products and co-products""; ""Magnus expansions and beyond""; ""Wilsonian renormalization, differential equations and Hopf algebras""; ""1. Introduction""; ""2. Basics of wilsonian renormalization""; ""3. Rooted trees and power series of non linear operators""; ""4. Renormalization, effective actions and Feynman diagrams""; ""5. Conclusion and outlook""; ""Acknowledgements""; ""References"" ""Algebraic analysis of non-renormalization theorems in supersymmetric field theories""""Not so non-renormalizable gravity""; ""Renormalised multiple zeta values which respect quasi-shuffle relations""; ""Formulas for the Connes�Moscovici Hopf algebra""; ""Hopf algebras and the combinatorics of connected graphs in quantum field theory""; ""Hopf Algebras of Formal Diffeomorphisms and Numerical Integration on Manifolds""; ""A combinatorial and field theoretic path to quantum gravity: The new challenges of group field theory"" ""Noncommutative formal Taylor expansions and second quantised regularised traces""""Motives: An introductory survey for physicists""; ""1. Introduction""; ""2. The Grothendieck ring""; ""3. The Tannakian formalism""; ""4. Weil cohomology""; ""5. Classical motives""; ""6. Mixed motives""; ""7. Motivic measures and zeta functions""; ""Appendix A. Motivic ideas in physics (by M.Marcolli)""; ""References""; ""Combinatorics and Feynman graphs for gauge theories""; ""Multi-scale Analysis and Non-commutative Field Theory"" |
| Record Nr. | UNINA-9910480290103321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2011] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Combinatorics and physics : Mini-Workshop on Renormalization, December 15-16, 2006, Max Planck Institut für Mathematik, Bonn, Germany : Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany / / Kurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom, editors
| Combinatorics and physics : Mini-Workshop on Renormalization, December 15-16, 2006, Max Planck Institut für Mathematik, Bonn, Germany : Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany / / Kurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2011] |
| Descrizione fisica | 1 online resource (480 p.) |
| Disciplina | 530.14/3 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Renormalization group
Quantum field theory Numerical integration |
| ISBN | 0-8218-8218-X |
| Classificazione | 81T1565D30 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Contents -- Preface -- List of participants -- One-particle irreducibility with initial correlations -- Multiple zeta values and periods: From moduli spaces to Feynman integrals -- From quantum electrodynamics to posets of planar binary trees -- Sweedler's duals and Schutzenberger's calculus -- Primitive elements of the Hopf algebra of free quasi-symmetric functions -- A Renormalisation Group approach to Stochastic Loewner Evolutions -- On the causal gauge principle -- 1. Introduction -- 2. Overview of the CGI method -- 3. The abelian model -- 4. Three MVBs -- 5. The Weinberg's alam model within CGI -- 6. Discussion -- References -- Abstract integration, combinatorics of trees and differential equations -- Rooted trees appearing in products and co-products -- Magnus expansions and beyond -- Wilsonian renormalization, differential equations and Hopf algebras -- 1. Introduction -- 2. Basics of wilsonian renormalization -- 3. Rooted trees and power series of non linear operators -- 4. Renormalization, effective actions and Feynman diagrams -- 5. Conclusion and outlook -- Acknowledgements -- References -- Algebraic analysis of non-renormalization theorems in supersymmetric field theories -- Not so non-renormalizable gravity -- Renormalised multiple zeta values which respect quasi-shuffle relations -- Formulas for the Connes-Moscovici Hopf algebra -- Hopf algebras and the combinatorics of connected graphs in quantum field theory -- Hopf Algebras of Formal Diffeomorphisms and Numerical Integration on Manifolds -- A combinatorial and field theoretic path to quantum gravity: The new challenges of group field theory -- Noncommutative formal Taylor expansions and second quantised regularised traces -- Motives: An introductory survey for physicists -- 1. Introduction -- 2. The Grothendieck ring -- 3. The Tannakian formalism -- 4. Weil cohomology -- 5. Classical motives -- 6. Mixed motives -- 7. Motivic measures and zeta functions -- Appendix A. Motivic ideas in physics (by M.Marcolli) -- References -- Combinatorics and Feynman graphs for gauge theories -- Multi-scale Analysis and Non-commutative Field Theory. |
| Record Nr. | UNINA-9910788633803321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2011] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Combinatorics and physics : Mini-Workshop on Renormalization, December 15-16, 2006, Max Planck Institut für Mathematik, Bonn, Germany : Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany / / Kurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom, editors
| Combinatorics and physics : Mini-Workshop on Renormalization, December 15-16, 2006, Max Planck Institut für Mathematik, Bonn, Germany : Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany / / Kurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2011] |
| Descrizione fisica | 1 online resource (480 p.) |
| Disciplina | 530.14/3 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Renormalization group
Quantum field theory Numerical integration |
| ISBN | 0-8218-8218-X |
| Classificazione | 81T1565D30 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Contents -- Preface -- List of participants -- One-particle irreducibility with initial correlations -- Multiple zeta values and periods: From moduli spaces to Feynman integrals -- From quantum electrodynamics to posets of planar binary trees -- Sweedler's duals and Schutzenberger's calculus -- Primitive elements of the Hopf algebra of free quasi-symmetric functions -- A Renormalisation Group approach to Stochastic Loewner Evolutions -- On the causal gauge principle -- 1. Introduction -- 2. Overview of the CGI method -- 3. The abelian model -- 4. Three MVBs -- 5. The Weinberg's alam model within CGI -- 6. Discussion -- References -- Abstract integration, combinatorics of trees and differential equations -- Rooted trees appearing in products and co-products -- Magnus expansions and beyond -- Wilsonian renormalization, differential equations and Hopf algebras -- 1. Introduction -- 2. Basics of wilsonian renormalization -- 3. Rooted trees and power series of non linear operators -- 4. Renormalization, effective actions and Feynman diagrams -- 5. Conclusion and outlook -- Acknowledgements -- References -- Algebraic analysis of non-renormalization theorems in supersymmetric field theories -- Not so non-renormalizable gravity -- Renormalised multiple zeta values which respect quasi-shuffle relations -- Formulas for the Connes-Moscovici Hopf algebra -- Hopf algebras and the combinatorics of connected graphs in quantum field theory -- Hopf Algebras of Formal Diffeomorphisms and Numerical Integration on Manifolds -- A combinatorial and field theoretic path to quantum gravity: The new challenges of group field theory -- Noncommutative formal Taylor expansions and second quantised regularised traces -- Motives: An introductory survey for physicists -- 1. Introduction -- 2. The Grothendieck ring -- 3. The Tannakian formalism -- 4. Weil cohomology -- 5. Classical motives -- 6. Mixed motives -- 7. Motivic measures and zeta functions -- Appendix A. Motivic ideas in physics (by M.Marcolli) -- References -- Combinatorics and Feynman graphs for gauge theories -- Multi-scale Analysis and Non-commutative Field Theory. |
| Record Nr. | UNINA-9910822705203321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2011] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An invitation to noncommutative geometry [[electronic resource] /] / editors, Masoud Khalkhali, Matilde Marcolli
| An invitation to noncommutative geometry [[electronic resource] /] / editors, Masoud Khalkhali, Matilde Marcolli |
| Pubbl/distr/stampa | New Jersey, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (515 p.) |
| Disciplina | 512/.55 |
| Altri autori (Persone) |
KhalkhaliMasoud <1956->
MarcolliMatilde |
| Soggetto topico | Noncommutative differential geometry |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-96811-0
9786611968113 981-281-433-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; A Walk in the Noncommutative Garden A. Connes and M. Marcolli; Contents; 1. Introduction; 2. Handling Noncommutative Spaces in the Wild: Basic Tools; 3. Phase Spaces of Microscopic Systems; 4. Noncommutative Quotients; 5. Spaces of Leaves of Foliations; 6. The Noncommutative Tori; 7. Duals of Discrete Groups; 8. Brillouin Zone and the Quantum Hall Effect; 9. Tilings; 10. Noncommutative Spaces from Dynamical Systems; 11. Noncommutative Spaces from String Theory; 12. Groupoids and the Index Theorem; 13. Riemannian Manifolds, Conical Singularities; 14. Cantor Sets and Fractals
15. Spaces of Dimension z and DimReg16. Local Algebras in Supersymmetric QFT; 17. Spacetime and the Standard Model of Elementary Particles; 18. Isospectral Deformations ; 19. Algebraic Deformations; 20. Quantum Groups; 21. Spherical Manifolds; 22. Q-lattices; 23. Modular Hecke Algebras; 24. Noncommutative Moduli Spaces, Shimura Varieties; 25. The Ad`ele Class Space and the Spectral Realization; 26. Thermodynamics of Endomotives and the Tehran Program; References; Renormalization of Noncommutative Quantum Field Theory H. Grosse and R. Wulkenhaar; Contents; 1. Introduction 1.1. Noncommutative geometry2. Some Models for Noncommutative Space(-Time); 2.1. The Moyal plane; 2.2. The noncommutative torus; 2.3. Fuzzy spaces; 3. Classical Field Theory on Noncommutative Spaces; 3.1. Field theory on the noncommutative torus; 3.2. Classical action functionals on the Moyal plane; 4. Regularization; 5. Renormalization; 5.1. Quantum field theory on the noncommutative torus; 5.2. Quantum field theories on the Moyal plane; 5.3. The power-counting analysis of Chepelev and Roiban; 5.4. -expanded field theories; 5.5. Noncommutative space-time 6. Renormalization of Noncommutative 4-theory to All Orders6.1. The 4-action in the matrix base; 6.2. Renormalization group approach to dynamical matrix models; 6.3. Power-counting behavior of the noncommutative 4-model; Acknowledgements; References; Lectures on Noncommutative Geometry M. Khalkhali; Contents; 1. Introduction; 2. From C -algebras to noncommutative spaces; 2.1. Gelfand-Naimark theorems; 2.2. GNS, KMS, and the ow of time; 2.3. From groups to noncommutative spaces; 2.4. Continuous fields of C -algebras; 2.5. Noncommutative tori; 3. Beyond C -algebras 3.1. Algebras stable under holomorphic functional calculus3.2. Almost commutative and Poisson algebras; 3.3. Deformation theory; 4. Sources of noncommutative spaces; 4.1. Noncommutative quotients; 4.2. Hopf algebras and quantum groups; 5. Topological K-theory; 5.1. The K functor; 5.2. The higher K-functors; 5.3. Bott periodicity theorem; 5.4. Further results; 5.5. Twisted K-theory; 5.6. K-homology; 6. Cyclic Cohomology; 6.1. Cyclic cocycles; 6.2. Connes' spectral sequence; 6.3. Topological algebras; 6.4. The deformation complex; 6.5. Cyclic homology; 6.6. Connes-Chern character 6.7. Cyclic modules |
| Record Nr. | UNINA-9910453537003321 |
| New Jersey, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An invitation to noncommutative geometry [[electronic resource] /] / editors, Masoud Khalkhali, Matilde Marcolli
| An invitation to noncommutative geometry [[electronic resource] /] / editors, Masoud Khalkhali, Matilde Marcolli |
| Pubbl/distr/stampa | New Jersey, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (515 p.) |
| Disciplina | 512/.55 |
| Altri autori (Persone) |
KhalkhaliMasoud <1956->
MarcolliMatilde |
| Soggetto topico | Noncommutative differential geometry |
| ISBN |
1-281-96811-0
9786611968113 981-281-433-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; A Walk in the Noncommutative Garden A. Connes and M. Marcolli; Contents; 1. Introduction; 2. Handling Noncommutative Spaces in the Wild: Basic Tools; 3. Phase Spaces of Microscopic Systems; 4. Noncommutative Quotients; 5. Spaces of Leaves of Foliations; 6. The Noncommutative Tori; 7. Duals of Discrete Groups; 8. Brillouin Zone and the Quantum Hall Effect; 9. Tilings; 10. Noncommutative Spaces from Dynamical Systems; 11. Noncommutative Spaces from String Theory; 12. Groupoids and the Index Theorem; 13. Riemannian Manifolds, Conical Singularities; 14. Cantor Sets and Fractals
15. Spaces of Dimension z and DimReg16. Local Algebras in Supersymmetric QFT; 17. Spacetime and the Standard Model of Elementary Particles; 18. Isospectral Deformations ; 19. Algebraic Deformations; 20. Quantum Groups; 21. Spherical Manifolds; 22. Q-lattices; 23. Modular Hecke Algebras; 24. Noncommutative Moduli Spaces, Shimura Varieties; 25. The Ad`ele Class Space and the Spectral Realization; 26. Thermodynamics of Endomotives and the Tehran Program; References; Renormalization of Noncommutative Quantum Field Theory H. Grosse and R. Wulkenhaar; Contents; 1. Introduction 1.1. Noncommutative geometry2. Some Models for Noncommutative Space(-Time); 2.1. The Moyal plane; 2.2. The noncommutative torus; 2.3. Fuzzy spaces; 3. Classical Field Theory on Noncommutative Spaces; 3.1. Field theory on the noncommutative torus; 3.2. Classical action functionals on the Moyal plane; 4. Regularization; 5. Renormalization; 5.1. Quantum field theory on the noncommutative torus; 5.2. Quantum field theories on the Moyal plane; 5.3. The power-counting analysis of Chepelev and Roiban; 5.4. -expanded field theories; 5.5. Noncommutative space-time 6. Renormalization of Noncommutative 4-theory to All Orders6.1. The 4-action in the matrix base; 6.2. Renormalization group approach to dynamical matrix models; 6.3. Power-counting behavior of the noncommutative 4-model; Acknowledgements; References; Lectures on Noncommutative Geometry M. Khalkhali; Contents; 1. Introduction; 2. From C -algebras to noncommutative spaces; 2.1. Gelfand-Naimark theorems; 2.2. GNS, KMS, and the ow of time; 2.3. From groups to noncommutative spaces; 2.4. Continuous fields of C -algebras; 2.5. Noncommutative tori; 3. Beyond C -algebras 3.1. Algebras stable under holomorphic functional calculus3.2. Almost commutative and Poisson algebras; 3.3. Deformation theory; 4. Sources of noncommutative spaces; 4.1. Noncommutative quotients; 4.2. Hopf algebras and quantum groups; 5. Topological K-theory; 5.1. The K functor; 5.2. The higher K-functors; 5.3. Bott periodicity theorem; 5.4. Further results; 5.5. Twisted K-theory; 5.6. K-homology; 6. Cyclic Cohomology; 6.1. Cyclic cocycles; 6.2. Connes' spectral sequence; 6.3. Topological algebras; 6.4. The deformation complex; 6.5. Cyclic homology; 6.6. Connes-Chern character 6.7. Cyclic modules |
| Record Nr. | UNINA-9910782273203321 |
| New Jersey, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An invitation to noncommutative geometry / / editors, Masoud Khalkhali, Matilde Marcolli
| An invitation to noncommutative geometry / / editors, Masoud Khalkhali, Matilde Marcolli |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | New Jersey, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (515 p.) |
| Disciplina | 512/.55 |
| Altri autori (Persone) |
KhalkhaliMasoud <1956->
MarcolliMatilde |
| Soggetto topico | Noncommutative differential geometry |
| ISBN |
1-281-96811-0
9786611968113 981-281-433-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; A Walk in the Noncommutative Garden A. Connes and M. Marcolli; Contents; 1. Introduction; 2. Handling Noncommutative Spaces in the Wild: Basic Tools; 3. Phase Spaces of Microscopic Systems; 4. Noncommutative Quotients; 5. Spaces of Leaves of Foliations; 6. The Noncommutative Tori; 7. Duals of Discrete Groups; 8. Brillouin Zone and the Quantum Hall Effect; 9. Tilings; 10. Noncommutative Spaces from Dynamical Systems; 11. Noncommutative Spaces from String Theory; 12. Groupoids and the Index Theorem; 13. Riemannian Manifolds, Conical Singularities; 14. Cantor Sets and Fractals
15. Spaces of Dimension z and DimReg16. Local Algebras in Supersymmetric QFT; 17. Spacetime and the Standard Model of Elementary Particles; 18. Isospectral Deformations ; 19. Algebraic Deformations; 20. Quantum Groups; 21. Spherical Manifolds; 22. Q-lattices; 23. Modular Hecke Algebras; 24. Noncommutative Moduli Spaces, Shimura Varieties; 25. The Ad`ele Class Space and the Spectral Realization; 26. Thermodynamics of Endomotives and the Tehran Program; References; Renormalization of Noncommutative Quantum Field Theory H. Grosse and R. Wulkenhaar; Contents; 1. Introduction 1.1. Noncommutative geometry2. Some Models for Noncommutative Space(-Time); 2.1. The Moyal plane; 2.2. The noncommutative torus; 2.3. Fuzzy spaces; 3. Classical Field Theory on Noncommutative Spaces; 3.1. Field theory on the noncommutative torus; 3.2. Classical action functionals on the Moyal plane; 4. Regularization; 5. Renormalization; 5.1. Quantum field theory on the noncommutative torus; 5.2. Quantum field theories on the Moyal plane; 5.3. The power-counting analysis of Chepelev and Roiban; 5.4. -expanded field theories; 5.5. Noncommutative space-time 6. Renormalization of Noncommutative 4-theory to All Orders6.1. The 4-action in the matrix base; 6.2. Renormalization group approach to dynamical matrix models; 6.3. Power-counting behavior of the noncommutative 4-model; Acknowledgements; References; Lectures on Noncommutative Geometry M. Khalkhali; Contents; 1. Introduction; 2. From C -algebras to noncommutative spaces; 2.1. Gelfand-Naimark theorems; 2.2. GNS, KMS, and the ow of time; 2.3. From groups to noncommutative spaces; 2.4. Continuous fields of C -algebras; 2.5. Noncommutative tori; 3. Beyond C -algebras 3.1. Algebras stable under holomorphic functional calculus3.2. Almost commutative and Poisson algebras; 3.3. Deformation theory; 4. Sources of noncommutative spaces; 4.1. Noncommutative quotients; 4.2. Hopf algebras and quantum groups; 5. Topological K-theory; 5.1. The K functor; 5.2. The higher K-functors; 5.3. Bott periodicity theorem; 5.4. Further results; 5.5. Twisted K-theory; 5.6. K-homology; 6. Cyclic Cohomology; 6.1. Cyclic cocycles; 6.2. Connes' spectral sequence; 6.3. Topological algebras; 6.4. The deformation complex; 6.5. Cyclic homology; 6.6. Connes-Chern character 6.7. Cyclic modules |
| Record Nr. | UNINA-9910826711403321 |
| New Jersey, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||