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Geometric and topological methods for quantum field theory : proceedings of the 2009 Villa de Leyva summer school / / edited by Alexander Cardona, Universidad de los Andes, Iván Contreras, University of Zurich, Andrés F. Reyes-Lega, Universidad de los Andes [[electronic resource]]
| Geometric and topological methods for quantum field theory : proceedings of the 2009 Villa de Leyva summer school / / edited by Alexander Cardona, Universidad de los Andes, Iván Contreras, University of Zurich, Andrés F. Reyes-Lega, Universidad de los Andes [[electronic resource]] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (x, 383 pages) : digital, PDF file(s) |
| Disciplina | 530.14/301516 |
| Soggetto topico |
Geometric quantization
Quantum field theory - Mathematics |
| ISBN |
1-107-23668-1
1-107-34432-8 1-107-34912-5 1-107-35769-1 1-107-34807-2 1-107-34557-X 1-139-20864-0 1-107-34182-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Contributors; Introduction; 1 A brief introduction to Dirac manifolds; 1.1 Introduction; 1.1.1 Notation, conventions, terminology; 1.2 Presymplectic and Poisson structures; 1.2.1 Two viewpoints on symplectic geometry; 1.2.2 Going degenerate; 1.3 Dirac structures; 1.4 Properties of Dirac structures; 1.4.1 Lie algebroid; 1.4.2 Presymplectic leaves and null distribution; 1.4.3 Hamiltonian vector fields and Poisson algebra; 1.5 Morphisms of Dirac manifolds; 1.5.1 Pulling back and pushing forward; 1.5.2 Clean intersection and smoothness issues
1.6 Submanifolds of Poisson manifolds and constraints1.6.1 The induced Poisson bracket on admissible functions; 1.6.2 A word on coisotropic submanifolds (or first-class constraints); 1.6.3 Poisson-Dirac submanifolds and the Dirac bracket; 1.6.4 Momentum level sets; 1.7 Brief remarks on further developments; Acknowledgments; References; 2 Differential geometry of holomorphic vector bundles on a curve; 2.1 Holomorphic vector bundles on Riemann surfaces; 2.1.1 Vector bundles; 2.1.2 Topological classification; 2.1.3 Dolbeault operators and the space of holomorphic structures; 2.1.4 Exercises 2.2 Holomorphic structures and unitary connections2.2.1 Hermitian metrics and unitary connections; 2.2.2 The Atiyah-Bott symplectic form; 2.2.3 Exercises; 2.3 Moduli spaces of semi-stable vector bundles; 2.3.1 Stable and semi-stable vector bundles; 2.3.2 Donaldson's theorem; 2.3.3 Exercises; References; 3 Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles; Introduction; Part 1: Some useful infinite dimensional Lie groups; 3.1 The gauge group of a bundle; 3.2 The diffeomorphism group of a bundle 3.3 The algebra of zero-order classical pseudodifferential operators3.4 The group of invertible zero-order dos; Part 2: Traces and central extensions; 3.5 Traces on zero-order classical dos; 3.6 Logarithms and central extensions; 3.7 Linear extensions of the L2-trace; Part 3: Singular Chern-Weil classes; 3.8 Chern-Weil calculus in finite dimensions; 3.9 A class of infinite dimensional vector bundles; 3.10 Frame bundles and associated do-algebra bundles; 3.11 Logarithms and closed forms; 3.12 Chern-Weil forms in infinite dimensions; 3.13 Weighted Chern--Weil forms; discrepancies 3.13.1 The Hochschild coboundary of a weighted trace3.13.2 Dependence on the weight; Part 4: Circumventing anomalies; 3.13.3 Exterior differential of a weighted trace; 3.13.4 Weighted traces extended to admissible fibre bundles; 3.13.5 Obstructions to closedness of weighted Chern--Weil forms; 3.14 Renormalised Chern-Weil forms on do Grassmannians; 3.15 Regular Chern-Weil forms in infinite dimensions; Acknowledgements; References; 4 Introduction to Feynman integrals; 4.1 Introduction; 4.2 Basics of perturbative quantum field theory; 4.3 Dimensional regularisation 4.4 Loop integration in D dimensions |
| Altri titoli varianti | Geometric & Topological Methods for Quantum Field Theory |
| Record Nr. | UNINA-9910462938203321 |
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometric and topological methods for quantum field theory : proceedings of the 2009 Villa de Leyva summer school / / edited by Alexander Cardona, Universidad de los Andes, Iván Contreras, University of Zurich, Andrés F. Reyes-Lega, Universidad de los Andes [[electronic resource]]
| Geometric and topological methods for quantum field theory : proceedings of the 2009 Villa de Leyva summer school / / edited by Alexander Cardona, Universidad de los Andes, Iván Contreras, University of Zurich, Andrés F. Reyes-Lega, Universidad de los Andes [[electronic resource]] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (x, 383 pages) : digital, PDF file(s) |
| Disciplina | 530.14/301516 |
| Soggetto topico |
Geometric quantization
Quantum field theory - Mathematics |
| ISBN |
1-107-23668-1
1-107-34432-8 1-107-34912-5 1-107-35769-1 1-107-34807-2 1-107-34557-X 1-139-20864-0 1-107-34182-5 |
| Classificazione | SCI040000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Contributors; Introduction; 1 A brief introduction to Dirac manifolds; 1.1 Introduction; 1.1.1 Notation, conventions, terminology; 1.2 Presymplectic and Poisson structures; 1.2.1 Two viewpoints on symplectic geometry; 1.2.2 Going degenerate; 1.3 Dirac structures; 1.4 Properties of Dirac structures; 1.4.1 Lie algebroid; 1.4.2 Presymplectic leaves and null distribution; 1.4.3 Hamiltonian vector fields and Poisson algebra; 1.5 Morphisms of Dirac manifolds; 1.5.1 Pulling back and pushing forward; 1.5.2 Clean intersection and smoothness issues
1.6 Submanifolds of Poisson manifolds and constraints1.6.1 The induced Poisson bracket on admissible functions; 1.6.2 A word on coisotropic submanifolds (or first-class constraints); 1.6.3 Poisson-Dirac submanifolds and the Dirac bracket; 1.6.4 Momentum level sets; 1.7 Brief remarks on further developments; Acknowledgments; References; 2 Differential geometry of holomorphic vector bundles on a curve; 2.1 Holomorphic vector bundles on Riemann surfaces; 2.1.1 Vector bundles; 2.1.2 Topological classification; 2.1.3 Dolbeault operators and the space of holomorphic structures; 2.1.4 Exercises 2.2 Holomorphic structures and unitary connections2.2.1 Hermitian metrics and unitary connections; 2.2.2 The Atiyah-Bott symplectic form; 2.2.3 Exercises; 2.3 Moduli spaces of semi-stable vector bundles; 2.3.1 Stable and semi-stable vector bundles; 2.3.2 Donaldson's theorem; 2.3.3 Exercises; References; 3 Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles; Introduction; Part 1: Some useful infinite dimensional Lie groups; 3.1 The gauge group of a bundle; 3.2 The diffeomorphism group of a bundle 3.3 The algebra of zero-order classical pseudodifferential operators3.4 The group of invertible zero-order dos; Part 2: Traces and central extensions; 3.5 Traces on zero-order classical dos; 3.6 Logarithms and central extensions; 3.7 Linear extensions of the L2-trace; Part 3: Singular Chern-Weil classes; 3.8 Chern-Weil calculus in finite dimensions; 3.9 A class of infinite dimensional vector bundles; 3.10 Frame bundles and associated do-algebra bundles; 3.11 Logarithms and closed forms; 3.12 Chern-Weil forms in infinite dimensions; 3.13 Weighted Chern--Weil forms; discrepancies 3.13.1 The Hochschild coboundary of a weighted trace3.13.2 Dependence on the weight; Part 4: Circumventing anomalies; 3.13.3 Exterior differential of a weighted trace; 3.13.4 Weighted traces extended to admissible fibre bundles; 3.13.5 Obstructions to closedness of weighted Chern--Weil forms; 3.14 Renormalised Chern-Weil forms on do Grassmannians; 3.15 Regular Chern-Weil forms in infinite dimensions; Acknowledgements; References; 4 Introduction to Feynman integrals; 4.1 Introduction; 4.2 Basics of perturbative quantum field theory; 4.3 Dimensional regularisation 4.4 Loop integration in D dimensions |
| Altri titoli varianti | Geometric & Topological Methods for Quantum Field Theory |
| Record Nr. | UNINA-9910786725703321 |
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometric and topological methods for quantum field theory : proceedings of the 2009 Villa de Leyva summer school / / edited by Alexander Cardona, Universidad de los Andes, Iván Contreras, University of Zurich, Andrés F. Reyes-Lega, Universidad de los Andes [[electronic resource]]
| Geometric and topological methods for quantum field theory : proceedings of the 2009 Villa de Leyva summer school / / edited by Alexander Cardona, Universidad de los Andes, Iván Contreras, University of Zurich, Andrés F. Reyes-Lega, Universidad de los Andes [[electronic resource]] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (x, 383 pages) : digital, PDF file(s) |
| Disciplina | 530.14/301516 |
| Soggetto topico |
Geometric quantization
Quantum field theory - Mathematics |
| ISBN |
1-107-23668-1
1-107-34432-8 1-107-34912-5 1-107-35769-1 1-107-34807-2 1-107-34557-X 1-139-20864-0 1-107-34182-5 |
| Classificazione | SCI040000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Contributors; Introduction; 1 A brief introduction to Dirac manifolds; 1.1 Introduction; 1.1.1 Notation, conventions, terminology; 1.2 Presymplectic and Poisson structures; 1.2.1 Two viewpoints on symplectic geometry; 1.2.2 Going degenerate; 1.3 Dirac structures; 1.4 Properties of Dirac structures; 1.4.1 Lie algebroid; 1.4.2 Presymplectic leaves and null distribution; 1.4.3 Hamiltonian vector fields and Poisson algebra; 1.5 Morphisms of Dirac manifolds; 1.5.1 Pulling back and pushing forward; 1.5.2 Clean intersection and smoothness issues
1.6 Submanifolds of Poisson manifolds and constraints1.6.1 The induced Poisson bracket on admissible functions; 1.6.2 A word on coisotropic submanifolds (or first-class constraints); 1.6.3 Poisson-Dirac submanifolds and the Dirac bracket; 1.6.4 Momentum level sets; 1.7 Brief remarks on further developments; Acknowledgments; References; 2 Differential geometry of holomorphic vector bundles on a curve; 2.1 Holomorphic vector bundles on Riemann surfaces; 2.1.1 Vector bundles; 2.1.2 Topological classification; 2.1.3 Dolbeault operators and the space of holomorphic structures; 2.1.4 Exercises 2.2 Holomorphic structures and unitary connections2.2.1 Hermitian metrics and unitary connections; 2.2.2 The Atiyah-Bott symplectic form; 2.2.3 Exercises; 2.3 Moduli spaces of semi-stable vector bundles; 2.3.1 Stable and semi-stable vector bundles; 2.3.2 Donaldson's theorem; 2.3.3 Exercises; References; 3 Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles; Introduction; Part 1: Some useful infinite dimensional Lie groups; 3.1 The gauge group of a bundle; 3.2 The diffeomorphism group of a bundle 3.3 The algebra of zero-order classical pseudodifferential operators3.4 The group of invertible zero-order dos; Part 2: Traces and central extensions; 3.5 Traces on zero-order classical dos; 3.6 Logarithms and central extensions; 3.7 Linear extensions of the L2-trace; Part 3: Singular Chern-Weil classes; 3.8 Chern-Weil calculus in finite dimensions; 3.9 A class of infinite dimensional vector bundles; 3.10 Frame bundles and associated do-algebra bundles; 3.11 Logarithms and closed forms; 3.12 Chern-Weil forms in infinite dimensions; 3.13 Weighted Chern--Weil forms; discrepancies 3.13.1 The Hochschild coboundary of a weighted trace3.13.2 Dependence on the weight; Part 4: Circumventing anomalies; 3.13.3 Exterior differential of a weighted trace; 3.13.4 Weighted traces extended to admissible fibre bundles; 3.13.5 Obstructions to closedness of weighted Chern--Weil forms; 3.14 Renormalised Chern-Weil forms on do Grassmannians; 3.15 Regular Chern-Weil forms in infinite dimensions; Acknowledgements; References; 4 Introduction to Feynman integrals; 4.1 Introduction; 4.2 Basics of perturbative quantum field theory; 4.3 Dimensional regularisation 4.4 Loop integration in D dimensions |
| Altri titoli varianti | Geometric & Topological Methods for Quantum Field Theory |
| Record Nr. | UNINA-9910810511103321 |
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometry, Topology and Operator Algebras : Global Analysis, Invariants and Their Significance in Theoretical Physics / / edited by Alexander Cardona, Andrés F. Reyes Lega
| Geometry, Topology and Operator Algebras : Global Analysis, Invariants and Their Significance in Theoretical Physics / / edited by Alexander Cardona, Andrés F. Reyes Lega |
| Edizione | [1st ed. 2025.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 |
| Descrizione fisica | 1 online resource (XIII, 281 p. 15 illus., 11 illus. in color.) |
| Disciplina | 530.1 |
| Collana | Mathematical Physics Studies |
| Soggetto topico |
Mathematical physics
Geometry, Algebraic Number theory Condensed matter Theoretical, Mathematical and Computational Physics Mathematical Physics Mathematical Methods in Physics Algebraic Geometry Number Theory Condensed Matter Physics |
| ISBN | 3-031-82319-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Geometric structures, invariants and their uses in physics by A. Cardona and A.F. Reyes-Lega -- . Lectures on the Euler characteristic of affine manifolds by Camilo Arias-Abad and Sebastian Velez-Vasquez -- Elliptic Curves by Philip Candelas -- The arithmetic of Calabi-Yau varieties, by Xenia de la Ossa -- Foliations and operator algebras by Georges Skandalis -- Pseudo-differential operators on groups and nonharmonic analysis, by Michael Ruzhansky -- Mathematical Foundations of Topological Matter, by Manuel Asorey. |
| Record Nr. | UNINA-9910999694903321 |
| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics / / edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega
| Quantization, Geometry and Noncommutative Structures in Mathematics and Physics / / edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (X, 341 p. 6 illus.) |
| Disciplina | 530.143 |
| Collana | Mathematical Physics Studies |
| Soggetto topico |
Quantum field theory
String models Mathematical physics Geometry, Algebraic Quantum Field Theories, String Theory Mathematical Physics Algebraic Geometry |
| ISBN | 3-319-65427-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Quantization, Geometry and Noncommutative Structures in Mathematics and Physics (A. Cardona, H. Ocampo, P. Morales, S. Paycha, A.F. Reyes Lega (Eds.)) -- General Overview (Alexander Cardona, Sylvie Paycha and Andrés F. Reyes Lega) -- Introduction -- Poisson Geometry and Classical Dynamics -- Geometric and Deformation Quantization -- Noncommutative Geometry and Quantum Groups -- Deformation Quantization and Group Actions (Simone Gutt) -- What do we mean by quantization? -- Deformation Quantization -- Fedosov’s star products on a symplectic manifold -- Classification of Poisson deformations and star products -- Star products on Poisson manifolds and formality -- Group actions in deformation quantization -- Reduction in deformation quantization -- Some remarks about convergence -- . Principal fiber bundles in non-commutative geometry (Christian Kassel) -- Introduction -- Review of principal fiber bundles -- Basic ideas of non-commutative geometry -- From groups to Hopf algebras -- Quantum groups associated with SL2(C) -- Group actions in non-commutative geometry -- Hopf Galois extensions -- Flat deformations of Hopf algebras -- An Introduction to Nichols Algebras (Nicolás Andruskiewitsch) -- Preliminaries -- Braided tensor categories -- Nichols algebras -- Classes of Nichols algebras -- Quantum Field Theory in Curved Space-Time (Andrés F. Reyes Lega) -- Introduction -- Quantum Field Theory in Minkowski Space-Time -- Quantum Field Theory in Curved Space-Time -- Cosmology -- An Introduction to Pure Spinor Superstring Theory (Nathan Berkovits and Humberto Gomez) -- Introduction -- Particle and Superparticle -- Pure Spinor Superstring -- Appendix -- Introduction to Elliptic Fibrations (Mboyo Esole) -- Introduction -- Elliptic curves over C -- Elliptic fibrations -- Kodaira-Néron classification of singular fibers -- Miranda models -- Batalin–Vilkovisky formalism as a theory of integration for polyvectors (Pierre J. Clavier and Viet Dang Nguyen) -- Motivations and program -- BV integral -- Gauge fixing -- Master equations -- Conclusion -- Split Chern-Simons theory in the BV-BFV formalism (Alberto S. Cattaneo, Pavel Mnev, and Konstantin Wernli) -- Introduction -- Overview of the BV and BV-BFV formalisms -- Chern-Simons theory as a BF-like theory -- Split Chern-Simons theory on the solid torus -- Conclusions and outlook -- Weighted direct product of spectral triples (Kevin Falk) -- Introduction and motivation. -Weighted direct product of spectral triples -- Example of weighted direct product with Toeplitz operators -- Index. |
| Record Nr. | UNINA-9910254593203321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||