Full Description
This open access book explains geometric quantization from a physicist's perspective. After presenting the general formalism, it delves into several examples reflecting current research interests in high-energy physics and condensed matter physics. Applications explore Chern-Simons theory, theta vacuum, the Hall effect, fluid dynamics, and elements of noncommutative geometry.
The content is tailored to appeal to researchers, graduate students, and advanced undergraduates in high-energy physics, particle physics, and mathematical physics. A background in differential geometry and group theory is beneficial for a comprehensive understanding of the discussions.
Contents
Introduction.- Symplectic Form and Poisson Brackets.- Classical Dynamics.- Geometric Quantization.- Topological Features of Quantization.- Coherent States, the Two-sphere and G/H Spaces.- The Chern-Simons Theory in 2+1 Dimensions.- θ-vacua in a Nonabelian Gauge Theory.- Fractional Statistics in Quantum Hall Effect.- Fluid Dynamics.- Quantization Rules.- A Comment on the Metaplectic Correction.
