Quantum Field Theory and Topology

Quantum Field Theory and Topology by Albert S. Schwarz.

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field th...

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Bibliographic Details
Main Author: Schwarz, Albert S. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993.
Edition:1st ed. 1993.
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 307
Springer eBook Collection.
Subjects:
Manifolds (Mathematics).
Complex manifolds.
Quantum physics.
Quantum computers.
Spintronics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Definitions and Notations
  • 1 The Simplest Lagrangians
  • 2 Quadratic Lagrangians
  • 3 Internal Symmetries
  • 4 Gauge Fields
  • 5 Particles Corresponding to Nonquadratic Lagrangians
  • 6 Lagrangians of Strong, Weak and Electromagnetic Interactions
  • 7 Grand Unifications
  • 8 Topologically Stable Defects
  • 9 Topological Integrals of Motion
  • 10 A Two-Dimensional Model. Abrikosov Vortices
  • 11 ’t Hooft—Polyakov Monopoles
  • 12 Topological Integrals of Motion in Gauge Theory
  • 13 Particles in Gauge Theories
  • 14 The Magnetic Charge
  • 15 Electromagnetic Field Strength and Magnetic Charge in Gauge Theories
  • 16 Extrema of Symmetric Functionals
  • 17 Symmetric Gauge Fields
  • 18 Estimates of the Energy of a Magnetic Monopole
  • 19 Topologically Non-Trivial Strings
  • 20 Particles in the Presence of Strings
  • 21 Nonlinear Fields
  • 22 Multivalued Action Integrals
  • 23 Functional Integrals
  • 24 Applications of Functional Integrals to Quantum Theory
  • 25 Quantization of Gauge Theories
  • 26 Elliptic Operators
  • 27 The Index and Other Properties of Elliptic Operators
  • 28 Determinants of Elliptic Operators
  • 29 Quantum Anomalies
  • 30 Instantons
  • 31 The Number of Instanton Parameters
  • 32 Computation of the Instanton Contribution
  • 33 Functional Integrals for a Theory Containing Fermion Fields
  • 34 Instantons in Quantum Chromodynamics
  • 35 Topological Spaces
  • 36 Groups
  • 37 Gluings
  • 38 Equivalence Relations and Quotient Spaces
  • 39 Group Representations
  • 40 Group Actions
  • 41 The Adjoint Representation of a Lie Group
  • 42 Elements of Homotopy Theory
  • 43 Applications of Topology to Physics
  • Bibliographical Remarks
  • References.

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