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Geometric and Topological Methods for Quantum Field Theory
 
Edited by: S. Paycha Université Blaise Pascal, Aubière, Cedex, France
B. Uribe Universidad de Los Andes, Bogatá, Columbia
Geometric and Topological Methods for Quantum Field Theory
eBook ISBN:  978-0-8218-8113-2
Product Code:  CONM/434.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Geometric and Topological Methods for Quantum Field Theory
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Geometric and Topological Methods for Quantum Field Theory
Edited by: S. Paycha Université Blaise Pascal, Aubière, Cedex, France
B. Uribe Universidad de Los Andes, Bogatá, Columbia
eBook ISBN:  978-0-8218-8113-2
Product Code:  CONM/434.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 4342007; 255 pp
    MSC: Primary 53; 55; 58; 81;

    This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures):

    • Anomalies and noncommutative geometry,
    • Deformation quantisation and Poisson algebras,
    • Topological quantum field theory and orbifolds.

    These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

    Readership

    Graduate students and research mathematicians interested in topological and geometric method in quantum field theory.

  • Table of Contents
     
     
    • Invited Lectures [ MR 2348965 ]
    • Martin Bordemann — Deformation quantization: a mini-lecture [ MR 2349629 ]
    • Giovanni Landi — Examples of noncommutative instantons [ MR 2349630 ]
    • Ernesto Lupercio and Bernardo Uribe — Topological quantum field theories, strings and orbifolds [ MR 2349631 ]
    • Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki and Akira Yoshioka — Non-formal deformation quantization of Fréchet-Poisson algebras: the Heisenberg and Lie algebra case [ MR 2349632 ]
    • Denis Perrot — Anomalies and noncommutative index theory [ MR 2349633 ]
    • Contributed talks [ MR 2348965 ]
    • Mauricio Ángel and Rafael Díaz — $N$-flat connections [ MR 2349634 ]
    • Alejandro Cáceres — Dirac equation in a black hole background [ MR 2349635 ]
    • Edmundo Castillo and Rafael Díaz — Homological matrices [ MR 2349636 ]
    • Andrei Giniatoulline and Oswaldo Zapata — On some qualitative properties of stratified flows [ MR 2349637 ]
    • Maria Paula Gomez-Aparicio — Property (T) and tensor products by irreducible finite dimensional representations for ${\rm SL}_n(\Bbb R)\ n\geq 3$ [ MR 2349638 ]
    • Richard Muñiz Manasliski — Painlevé VI equation from invariant instantons [ MR 2349639 ]
    • Jorge Plazas — Quantum statistical mechanics and class field theory [ MR 2349640 ]
    • Pietro Polesello — Uniqueness of Kashiwara’s quantization of complex contact manifolds [ MR 2349641 ]
    • Fonger Ypma — $K$-theoretic gap labeling for quasicrystals [ MR 2349642 ]
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 4342007; 255 pp
MSC: Primary 53; 55; 58; 81;

This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures):

  • Anomalies and noncommutative geometry,
  • Deformation quantisation and Poisson algebras,
  • Topological quantum field theory and orbifolds.

These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

Readership

Graduate students and research mathematicians interested in topological and geometric method in quantum field theory.

  • Invited Lectures [ MR 2348965 ]
  • Martin Bordemann — Deformation quantization: a mini-lecture [ MR 2349629 ]
  • Giovanni Landi — Examples of noncommutative instantons [ MR 2349630 ]
  • Ernesto Lupercio and Bernardo Uribe — Topological quantum field theories, strings and orbifolds [ MR 2349631 ]
  • Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki and Akira Yoshioka — Non-formal deformation quantization of Fréchet-Poisson algebras: the Heisenberg and Lie algebra case [ MR 2349632 ]
  • Denis Perrot — Anomalies and noncommutative index theory [ MR 2349633 ]
  • Contributed talks [ MR 2348965 ]
  • Mauricio Ángel and Rafael Díaz — $N$-flat connections [ MR 2349634 ]
  • Alejandro Cáceres — Dirac equation in a black hole background [ MR 2349635 ]
  • Edmundo Castillo and Rafael Díaz — Homological matrices [ MR 2349636 ]
  • Andrei Giniatoulline and Oswaldo Zapata — On some qualitative properties of stratified flows [ MR 2349637 ]
  • Maria Paula Gomez-Aparicio — Property (T) and tensor products by irreducible finite dimensional representations for ${\rm SL}_n(\Bbb R)\ n\geq 3$ [ MR 2349638 ]
  • Richard Muñiz Manasliski — Painlevé VI equation from invariant instantons [ MR 2349639 ]
  • Jorge Plazas — Quantum statistical mechanics and class field theory [ MR 2349640 ]
  • Pietro Polesello — Uniqueness of Kashiwara’s quantization of complex contact manifolds [ MR 2349641 ]
  • Fonger Ypma — $K$-theoretic gap labeling for quasicrystals [ MR 2349642 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.