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Geometric and topological methods for quantum field theory / edited by Hernán Ocampo, Eddy Pariguán, Sylvie Paycha.

Contributor(s): Ocampo, Hernán | Pariguán, Eddy | Paycha, SylvieMaterial type: TextTextPublication details: New York : Cambridge University Press, 2010. Description: 1 online resource (xii, 421 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9780511712883; 051171288X; 9780521764827; 0521764823; 9781282637252; 1282637258Subject(s): Geometry, Differential | Quantum theory | SCIENCE -- Waves & Wave Mechanics | Geometry, Differential | Quantum theoryGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Geometric and topological methods for quantum field theory.DDC classification: 530.14/301516 LOC classification: QC20.7.D52 | G46 2010ebOnline resources: Click here to access online
Contents:
Introduction -- 1. The impact of QFT on low-dimensional topology / Paul Kirk -- 2. Differential equations aspects of quantum cohomology / Martin A. Guest -- 3. Index theory and groupoids / Claire Debord and Jean-Marie Lescure -- 4. Renormalization Hopf algebras and combinatorial groups / Alessandra Frabetti -- 5. BRS invariance for massive boson fields / José M. Gracia-Bondía -- 6. Large N field theories and geometry / David Berenstein -- 7. Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity / Martin Reuter and Frank Saueressig -- 8. When is a differentiable manifold the boundary of an orbifold? / Andrés Angel -- 9. Canonical group quantization, rotation generators and quantum indistinguishability / Carlos Benavides and Andrés Reyes-Lega -- 10. Conserved currents in Kähler manifolds / Jaime R. Camacaro and Juan Carlos Moreno -- 11. A symmetrized canonical determinant on odd-class pseudodifferential operators / Marie-Françoise Ouedraogo -- 12. Some remarks about cosymplectic metrics on maximal flag manifolds / Marlio Paredes and Sofia Pinzón -- 13. Heisenberg modules over real multiplication noncommutative tori and related algebraic structures / Jorge Plazas.
Summary: "Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest"--Provided by publisher.
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Includes bibliographical references and index.

"Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest"--Provided by publisher.

Print version record.

Introduction -- 1. The impact of QFT on low-dimensional topology / Paul Kirk -- 2. Differential equations aspects of quantum cohomology / Martin A. Guest -- 3. Index theory and groupoids / Claire Debord and Jean-Marie Lescure -- 4. Renormalization Hopf algebras and combinatorial groups / Alessandra Frabetti -- 5. BRS invariance for massive boson fields / José M. Gracia-Bondía -- 6. Large N field theories and geometry / David Berenstein -- 7. Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity / Martin Reuter and Frank Saueressig -- 8. When is a differentiable manifold the boundary of an orbifold? / Andrés Angel -- 9. Canonical group quantization, rotation generators and quantum indistinguishability / Carlos Benavides and Andrés Reyes-Lega -- 10. Conserved currents in Kähler manifolds / Jaime R. Camacaro and Juan Carlos Moreno -- 11. A symmetrized canonical determinant on odd-class pseudodifferential operators / Marie-Françoise Ouedraogo -- 12. Some remarks about cosymplectic metrics on maximal flag manifolds / Marlio Paredes and Sofia Pinzón -- 13. Heisenberg modules over real multiplication noncommutative tori and related algebraic structures / Jorge Plazas.

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