Bibliothèque de L'IMIST/CNRST

Includes bibliographical references and index.

Examples of Quantizations -- Quantization of R[superscript 2] -- Classical mechanics -- Symplectic method -- Holomorphic method -- Holomorphic representation of symplectic quotients and its quantization -- An example of circle action -- Moment map of symplectic actions -- Some geometric invariant theory -- Grassmanians -- Calabi-Yau/Ginzburg-Landau correspondence -- Quantization of symplectic quotients -- Classical Solutions of Gauge Field Theory -- Moduli space of classical solutions of Chern-Simons action -- Symplectic reduction of gauge fields over a Riemann surface -- Chern-Simons action on a three manifold -- Maxwell equations and Yang-Mills equations -- Maxwell equations -- Yang-Mills equations -- Vector bundle, Chern classes and Chern-Weil theory -- Vector bundle and connection -- Curvature, Chern classes and Chern-Weil theory -- Quantization of Chern-Simons Action -- Some formal discussions on quantization -- Pre-quantization -- M as a complex variety -- Quillen's determinant bundle on M and the Laplacian -- Some Lie groups -- G = R -- G = S[superscript 1] = R/2[pi]Z -- T*G -- Compact Lie groups, G = SU (2) -- Genus one -- Riemann sphere with punctures -- Higher genus Riemann surface -- Relation with WZW model and conformal field theory -- Independence of complex structures -- Borel-Weil-Bott theorem of representation of Lie groups -- Chern-Simons-Witten Theory and Three Manifold Invariant -- Representation of mapping class group and three manifold invariant -- Knizhik-Zamolodchikov equations and conformal blocks.