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E-grāmata: Geometric and Topological Methods for Quantum Field Theory: Proceedings of the 2009 Villa de Leyva Summer School

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Edited by (Universidad de los Andes, Colombia), Edited by (Universidad de los Andes, Colombia), Edited by (Universität Zürich)
  • Formāts: PDF+DRM
  • Izdošanas datums: 09-May-2013
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781107352698
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Geometric and Topological Methods for Quantum Field Theory: Proceedings of the 2009 Villa de Leyva Summer SchoolPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 09-May-2013
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781107352698
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"Based on lectures given at the renowed Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics"--

Recenzijas

' a valuable guide for graduate students and researchers in physics and mathematics ' CERN Courier

Papildus informācija

A unique presentation of modern geometric methods in quantum field theory for researchers and graduate students in mathematics and physics.
List of contributors
ix
Introduction 1(3)
1 A brief introduction to Dirac manifolds
4(35)
Henrique Bursztyn
1.1 Introduction
4(2)
1.2 Presymplectic and Poisson structures
6(5)
1.3 Dirac structures
11(3)
1.4 Properties of Dirac structures
14(2)
1.5 Morphisms of Dirac manifolds
16(10)
1.6 Submanifolds of Poisson manifolds and constraints
26(7)
1.7 Brief remarks on further developments
33(6)
References
36(3)
2 Differential geometry of holomorphic vector bundles on a curve
39(42)
Florent Schaffhauser
2.1 Holomorphic vector bundles on Riemann surfaces
39(14)
2.2 Holomorphic structures and unitary connections
53(14)
2.3 Moduli spaces of semi-stable vector bundles
67(14)
References
79(2)
3 Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles
81(63)
Sylvie Paycha
3.1 The gauge group of a bundle
85(2)
3.2 The diffeomorphism group of a bundle
87(1)
3.3 The algebra of zero-order classical pseudodifferential operators
88(6)
3.4 The group of invertible zero-order dos
94(6)
3.5 Traces on zero-order classical dos
100(2)
3.6 Logarithms and central extensions
102(5)
3.7 Linear extensions of the L2-trace
107(8)
3.8 Chern-Weil calculus in finite dimensions
115(2)
3.9 A class of infinite dimensional vector bundles
117(2)
3.10 Frame bundles and associated do-algebra bundles
119(4)
3.11 Logarithms and closed forms
123(2)
3.12 Chern-Weil forms in infinite dimensions
125(2)
3.13 Weighted Chern-Weil forms; discrepancies
127(5)
3.14 Renormalised Chern-Weil forms on do Grassmannians
132(3)
3.15 Regular Chern-Weil forms in infinite dimensions
135(9)
References
139(5)
4 Introduction to Feynman integrals
144(44)
Stefan Weinzierl
4.1 Introduction
144(2)
4.2 Basics of perturbative quantum field theory
146(8)
4.3 Dimensional regularisation
154(3)
4.4 Loop integration in D dimensions
157(6)
4.5 Multi-loop integrals
163(2)
4.6 How to obtain finite results
165(5)
4.7 Feynman integrals and periods
170(1)
4.8 Shuffle algebras
171(5)
4.9 Multiple polylogarithms
176(2)
4.10 From Feynman integrals to multiple polylogarithms
178(6)
4.11 Conclusions
184(4)
References
185(3)
5 Iterated integrals in quantum field theory
188(53)
Francis Brown
5.1 Introduction
188(2)
5.2 Definition and first properties of iterated integrals
190(8)
5.3 The case P1/(0, 1, oo) and polylogarithms
198(5)
5.4 The KZ equation and the monodromy of polylogarithms
203(5)
5.5 A brief overview of multiple zeta values
208(6)
5.6 Iterated integrals and homotopy invariance
214(8)
5.7 Feynman integrals
222(19)
References
239(2)
6 Geometric issues in quantum field theory and string theory
241(33)
Luis J. Boya
6.1 Differential geometry for physicists
241(12)
6.2 Holonomy
253(7)
6.3 Strings and higher dimensions
260(7)
6.4 Some issues on compactification
267(7)
Exercises
272(1)
References
273(1)
7 Geometric aspects of the Standard Model and the mysteries of matter
274(33)
Florian Scheck
7.1 Radiation and matter in gauge theories and General Relativity
274(10)
7.2 Mass matrices and state mixing
284(5)
7.3 The space of connections and the action functional
289(4)
7.4 Constructions within noncommutative geometry
293(4)
7.5 Further routes to quantization via BRST symmetry
297(4)
7.6 Some conclusions and outlook
301(6)
Exercises
302(1)
Appendix: Proof of relation (7.11a)
303(2)
References
305(2)
8 Absence of singular continuous spectrum for some geometric Laplacians
307(15)
Leonardo A. Cano Garcia
8.1 Meromorphic extension of the resolvent and singular continuous spectrum
309(4)
8.2 Analytic dilation on complete manifolds with corners of codimension 2
313(9)
References
320(2)
9 Models for formal groupoids
322(18)
Ivan Contreras
9.1 Motivation and plan
322(1)
9.2 Definitions and examples
323(5)
9.3 Algebraic structure for formal groupoids
328(8)
9.4 The symplectic case
336(4)
References
339(1)
10 Elliptic PDEs and smoothness of weakly Einstein metrics of Holder regularity
340(26)
Andres Vargas
10.1 Introduction
340(1)
10.2 Basics on function spaces
341(6)
10.3 Elliptic operators and PDEs
347(8)
10.4 Riemannian regularity and harmonic coordinates
355(5)
10.5 Ricci curvature and the Einstein condition
360(6)
References
365(1)
11 Regularized traces and the index formula for manifolds with boundary
366(13)
Alexander Cardona
Cesar Del Corral
11.1 General heat kernel expansions and zeta functions
368(3)
11.2 Weighted traces, weighted trace anomalies and index terms
371(5)
11.3 Eta-invariant and super-traces
376(3)
Acknowledgements 379(1)
References 379(2)
Index 381
Alexander Cardona is Associate Professor in Mathematics, Universidad de los Andes, Bogotį, where he is part of the research group in geometry, topology and global analysis. His research interest includes a wide range of applications of mathematics in theoretical physics. Ivįn Contreras is a PhD student at the Institute of Mathematics, University of Zurich, working in the mathematical physics group. His areas of interest cover the connection between geometry, topology and field theories. Andrés F. Reyes-Lega is Associate Professor at the Physics Department, Universidad de los Andes, Bogotį, and is a member of the theoretical physics group. His recent research work has been in quantum field theory and quantum information theory.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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