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Chern-Simons Gauge Theory: 20 Years After
 
Edited by: Jørgen E. Andersen :  Aarhus University, Aarhus, Denmark
Hans U. Boden :  McMaster University, Hamilton, ON, Canada
Atle Hahn :  Universidade de Lisboa, Lisboa, Portugal
Benjamin Himpel :  Universität Bonn, Bonn, Germany
A co-publication of the AMS and International Press of Boston
Chern-Simons Gauge Theory: 20 Years After
Softcover ISBN:  978-0-8218-5353-5
Product Code:  AMSIP/50
List Price: $154.00
MAA Member Price: $138.60
AMS Member Price: $123.20
eBook ISBN:  978-1-4704-1753-6
Product Code:  AMSIP/50.E
List Price: $144.00
MAA Member Price: $129.60
AMS Member Price: $115.20
Softcover ISBN:  978-0-8218-5353-5
eBook: ISBN:  978-1-4704-1753-6
Product Code:  AMSIP/50.B
List Price: $298.00 $226.00
MAA Member Price: $268.20 $203.40
AMS Member Price: $238.40 $180.80
Add to cart
Chern-Simons Gauge Theory: 20 Years After
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Chern-Simons Gauge Theory: 20 Years After
Edited by: Jørgen E. Andersen :  Aarhus University, Aarhus, Denmark
Hans U. Boden :  McMaster University, Hamilton, ON, Canada
Atle Hahn :  Universidade de Lisboa, Lisboa, Portugal
Benjamin Himpel :  Universität Bonn, Bonn, Germany
A co-publication of the AMS and International Press of Boston
Softcover ISBN:  978-0-8218-5353-5
Product Code:  AMSIP/50
List Price: $154.00
MAA Member Price: $138.60
AMS Member Price: $123.20
eBook ISBN:  978-1-4704-1753-6
Product Code:  AMSIP/50.E
List Price: $144.00
MAA Member Price: $129.60
AMS Member Price: $115.20
Softcover ISBN:  978-0-8218-5353-5
eBook ISBN:  978-1-4704-1753-6
Product Code:  AMSIP/50.B
List Price: $298.00 $226.00
MAA Member Price: $268.20 $203.40
AMS Member Price: $238.40 $180.80
Add to cart
  • Book Details
     
     
    AMS/IP Studies in Advanced Mathematics
    Volume: 50; 2011; 446 pp
    MSC: Primary 11; 14; 16; 19; 20; 30; 32; 46; 53

    In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory.

    The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.

    Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.
    Readership

    Graduate students and research mathematicians interested in mathematical physics; topological quantum field theory; Chern-Simons theory.
  • Table of Contents
     
     
    • Chapters
    • Remarks on Wilson loops and Seifert loops in Chern-Simons theory
    • Quantum field theory and the volume conjecture
    • Computational aspects in Reidemeister torsion and Chern-Simons theories
    • Functional integration and abelian link invariants
    • Chern-Simons invariants, SO(3) instantons, and $\mathbb {Z}/2$ homology cobordism
    • Extending the $SU(3)$ Casson invariant to rational homology 3-spheres
    • Decomposition of Witten-Reshetikhin-Turaev invariant: Linking pairing and modular forms
    • Representations and the colored Jones polynomial of a torus knot
    • Eta-invariants and anomalies in $U/1$ Chern-Simons theory
    • Delta-groupoids and ideal triangulations
    • Invariants of knots and 3-manifolds derived from the equivariant linking pairing
    • Chern-Simons theory, the $1/N$ expansion, and string theory
    • Global Lorentzian geometry from lightlike geodesics: What does an observer in (2+1)-gravity see?
    • Spin foam state sums and Chern-Simons theory
    • Representations of the Ptolemy groupoid, Johnson homomorphisms, and finite type invariants
    • Yang-Mills in two dimensions and Chern-Simons in three
    • Intersection pairings on spaces of connections and Chern-Simons theory on Seifert manifolds
    • Fermionization and convergent perturbation expansions in Chern-Simons gauge theory
    • Analytic continuation of Chern-Simons theory
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
AMS/IP Studies in Advanced Mathematics
Volume: 50; 2011; 446 pp
MSC: Primary 11; 14; 16; 19; 20; 30; 32; 46; 53

In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory.

The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.
Readership

Graduate students and research mathematicians interested in mathematical physics; topological quantum field theory; Chern-Simons theory.
  • Chapters
  • Remarks on Wilson loops and Seifert loops in Chern-Simons theory
  • Quantum field theory and the volume conjecture
  • Computational aspects in Reidemeister torsion and Chern-Simons theories
  • Functional integration and abelian link invariants
  • Chern-Simons invariants, SO(3) instantons, and $\mathbb {Z}/2$ homology cobordism
  • Extending the $SU(3)$ Casson invariant to rational homology 3-spheres
  • Decomposition of Witten-Reshetikhin-Turaev invariant: Linking pairing and modular forms
  • Representations and the colored Jones polynomial of a torus knot
  • Eta-invariants and anomalies in $U/1$ Chern-Simons theory
  • Delta-groupoids and ideal triangulations
  • Invariants of knots and 3-manifolds derived from the equivariant linking pairing
  • Chern-Simons theory, the $1/N$ expansion, and string theory
  • Global Lorentzian geometry from lightlike geodesics: What does an observer in (2+1)-gravity see?
  • Spin foam state sums and Chern-Simons theory
  • Representations of the Ptolemy groupoid, Johnson homomorphisms, and finite type invariants
  • Yang-Mills in two dimensions and Chern-Simons in three
  • Intersection pairings on spaces of connections and Chern-Simons theory on Seifert manifolds
  • Fermionization and convergent perturbation expansions in Chern-Simons gauge theory
  • Analytic continuation of Chern-Simons theory
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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