Birmingham Danny, Blau Matthias, Rakowski Mark, Thompson George. Topological Field Theory

Elsevier Science Publishers, 1991. — 212 p.General aspects of topological field theory
Definitions
Moduli space as fields, equations, and
symmetries
Supersymmetric quantum mechanicsToy model
Nicolai map
Toy model
General model
Langevin approach
Toy model
General model
Quantizing zero
Toy model
General model
Metric independence
BRST symmetry and physical states
Physical states in supersymmetric theories
Physical states in gauge theories
Physical states in topological field theories
The toy model in detail
The Witten index
Path integral representation
The Euler character
A brief review of de Rham theory and Witten's generalization
Path integral representation of the Euler character
Supersymmetry and the Laplacian
The Poincare-Hopf theorem
The Gauss-Bonnet theorem
General properties of the Euler character
Symmetry breaking and zero modes
Zero modes of the toy model
Symmetry breaking and zero modes
Gauge and metric independence
The general model
Morse theory and supersymmetry
The weak Morse inequalities
The Witten complex and Morse theory
Topological sigma modelsReview of complex manifolds
Mathematical motivation
Construction and properties of the model
The Langevin approach
The Baulieu-Singer approach
The Nicolai map
A more general model
Nicolai maps and Backlund
transformations
The O(3) supersymmetric sigma model
Generalizations
Construction of observables
Moduli space and the ghost number anomaly
Observables and intersection theory
Topological gauge theories of Witten type
Mathematical backgroundGeometry of gauge theories
Spaces of connections
Instanton moduli space
Topology of four-manifolds and
Donaldson invariants
Floer homology and Morse theory
Donaldson theory
Fundamental properties
The approach of Baulieu-Singer and
Brooks-Montano-Sonnenschein
The Labastida-Pernici approach
Other approaches
Evaluation of the partition function
The Atiyah-Jeffrey interpretation
Construction of observables
Observables as differential forms on moduli space
The Hamiltonian point of view
Geometry of topological gauge theories
The universal bundle
Geometry of Donaldson theory
Observables and triviality
Construction of topological gauge theories
The classical action
The quantum action
Moduli spaces of flat connections I
Observables and the Casson invariant
Schwarz type topological gauge theories
Chern-Simons theory
Action, symmetries and observables
Phase space
Evaluation of the partition function
Evaluation of the observables: knot invariants
Connections with conformal field theory
BF theories
Quantization of Abelian BF theories
Observables in Abelian BF theories
Classical aspects of non-Abelian BF theories
Quantization of non-Abelian BF theories
Nicolai maps and Yang-Mills theory
The self-duality equations on a Riemann surface
Moduli spaces of flat connections II: PSL(2,R)
Topological gravity and self-duality
Topological gravityTwo-dimensional gravity
The Labastida-Pernici-Witten action
Relationship with quantum gravity and matrix models
A gauge theory of topological gravity
Gauge theory observables
RenormalizationDonaldson theory at one loop
Topological sigma models at one loop
Renormalization in Chern-Simons theory
Regularization of determinants
Chern-Simons theory at one loop
Evaluation of the phase
Gauge dependence of the effective action
Physical relevance of the results
Chern-Simons supersymmetry
Appendices
The Batalin-Vilkovisky quantization procedure
Donaldson theory
Supersymmetric quantum mechanics
Topological sigma models
Batalin-Vilkovisky triangles
Conventions