عنوان

Geometric and topological methods for quantum field theory :

(Number (ISBN

1107341825

(Number (ISBN

110734557X

(Number (ISBN

1107348072

(Number (ISBN

1139208640

(Number (ISBN

1299634869

(Number (ISBN

9781107341821

(Number (ISBN

9781107345577

(Number (ISBN

9781107348073

(Number (ISBN

9781139208642

(Number (ISBN

9781299634862

Erroneous ISBN

1107026830

Erroneous ISBN

9781107026834

Title Proper

Geometric and topological methods for quantum field theory :

General Material Designation

[Book]

Other Title Information

proceedings of the 2009 Villa de Leyva summer school /

First Statement of Responsibility

edited by Alexander Cardona, Iván Contreras, Andrés F. Reyes-Lega.

Place of Publication, Distribution, etc.

Cambridge :

Name of Publisher, Distributor, etc.

Cambridge University Press,

Date of Publication, Distribution, etc.

2013.

Specific Material Designation and Extent of Item

1 online resource

Text of Note

Includes bibliographical references and index.

Text of Note

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

Text of Note

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

Text of Note

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

Text of Note

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

Text of Note

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

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Text of Note

"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"--

Source for Acquisition/Subscription Address

Safari Books Online

Stock Number

CL0500000265

Title

Geometric and topological methods for quantum field theory.

International Standard Book Number

9781107026834

Geometric quantization.

Quantum field theory-- Mathematics.

Geometric quantization.

Quantum field theory-- Mathematics.

SCIENCE-- Mathematical Physics.

SCIENCE-- Waves & Wave Mechanics.

SCI-- 067000

Number

Edition

Class number

Book number

Class number

System Code

Cardona, Alexander

Contreras, Iván,1985-

Reyes-Lega, Andrés F.,1973-

Date of Transaction

20200822170355.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y