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Gauge Theory on Compact Surfaces
 
Ambar Sengupta Lousiana State University, Baton Rouge, LA
Gauge Theory on Compact Surfaces
eBook ISBN:  978-1-4704-0185-6
Product Code:  MEMO/126/600.E
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
Gauge Theory on Compact Surfaces
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Gauge Theory on Compact Surfaces
Ambar Sengupta Lousiana State University, Baton Rouge, LA
eBook ISBN:  978-1-4704-0185-6
Product Code:  MEMO/126/600.E
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1261997; 85 pp
    MSC: Primary 81;

    This work presents a rigorous account of quantum gauge field theory for bundles (both trivial and non-trivial) over compact surfaces. The Euclidean quantum field measure describing this theory is constructed and loop expectation values for a broad class of Wilson loop configurations are computed explicitly. Both the topology of the surface and the topology of the bundle are encoded in these loop expectation values. The effect of well-behaved area-preserving homeomorphisms of the surface is to take these loop expectation values into those for the pullback bundle. The quantum gauge field measure is constructed by conditioning an infinite-dimensional Gaussian measure to satisfy constraints imposed by the topologies of the surface and of the bundle. Holonomies, in this setting, are defined by interpreting the usual parallel-transport equation as a stochastic differential equation.

    Readership

    Graduate students, research mathematicians and physicists interested in quantum field theory, gauge theory or stochastic geometry.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Terminology and basic facts
    • 3. The structure of bundles and connections over compact surfaces
    • 4. Quantum gauge theory on the disk
    • 5. A conditional probability measure
    • 6. The Yang-Mills measure
    • 7. Invariants of systems of curves
    • 8. Loop expectation values I
    • 9. Some tools for the abelian case
    • 10. Loop expectation values II
    • Appendix
  • 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: 1261997; 85 pp
MSC: Primary 81;

This work presents a rigorous account of quantum gauge field theory for bundles (both trivial and non-trivial) over compact surfaces. The Euclidean quantum field measure describing this theory is constructed and loop expectation values for a broad class of Wilson loop configurations are computed explicitly. Both the topology of the surface and the topology of the bundle are encoded in these loop expectation values. The effect of well-behaved area-preserving homeomorphisms of the surface is to take these loop expectation values into those for the pullback bundle. The quantum gauge field measure is constructed by conditioning an infinite-dimensional Gaussian measure to satisfy constraints imposed by the topologies of the surface and of the bundle. Holonomies, in this setting, are defined by interpreting the usual parallel-transport equation as a stochastic differential equation.

Readership

Graduate students, research mathematicians and physicists interested in quantum field theory, gauge theory or stochastic geometry.

  • Chapters
  • 1. Introduction
  • 2. Terminology and basic facts
  • 3. The structure of bundles and connections over compact surfaces
  • 4. Quantum gauge theory on the disk
  • 5. A conditional probability measure
  • 6. The Yang-Mills measure
  • 7. Invariants of systems of curves
  • 8. Loop expectation values I
  • 9. Some tools for the abelian case
  • 10. Loop expectation values II
  • Appendix
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.