Parameswaran N. Geometric Quantization and Applications to Fields...Fluids 2024

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Parameswaran N. Geometric Quantization and Applications to Fields...Fluids 2024

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Textbook in PDF format Preface Introduction Symplectic Form and Poisson Brackets Symplectic Structure Poisson Brackets Phase Volume Darboux's Theorem Classical Dynamics Geometric Quantization Pre-Quantization Polarization Measure of Integration Representation of Operators Comments on the Measure of Integration, Corrected Operators, Etc Topological Features of Quantization The Case of Nontrivial script upper H Superscript 1 Baseline left parenthesis upper M comma double struck upper R right parenthesismathcalH1(M, mathbbR) The Case of Nontrivial script upper H squared left parenthesis upper M comma double struck upper R right parenthesismathcalH2(M, mathbbR) Summary of Holomorphic Polarization and Quantization Coherent States, the Two-Sphere and upper G divided by upper HG/H Spaces Coherent States Quantizing the Two-Sphere Quantization Using Local Coordinates Quantization Using Homogeneous Coordinates Group Theoretic Version Kähler Spaces of the upper G divided by upper HG/H-Type Quantizing double struck upper C upper P squaredmathbbCP2 Quantizing General upper G divided by upper HG/H Spaces A Note on an Index Theorem A Short Historical Note The Chern-Simons Theory in 2+1 Dimensions Analysis on upper S squared times double struck upper RS2 timesmathbbR Argument for Quantization of kk The Ground State Wave Function Abelian Theory on the Torus thetaθ-Vacua in a Nonabelian Gauge Theory Fractional Statistics in Quantum Hall Effect Quantum Hall Effect and the Landau Problem Excitations in Fractional QHE Fluid Dynamics The Lagrange Formulation Clebsch Variables and the General Form of Action Assorted Comments Examples Nonabelian Magnetohydrodynamics Spin and Fluids Anomalies in Fluid Dynamics Anomalous Electrodynamics Anomalies in the Fluid Phase of the Standard Model The Chiral Magnetic Effect Quantization Rules A Comment on the Metaplectic Correction Solutions to Problems References Index