Geometric Quantization: Particles, Fields and Strings

TL;DR

This paper introduces geometric quantization, illustrating its application to particles, fields, and strings, emphasizing physical motivation and interpretation within a formal mathematical framework.

Contribution

It provides a detailed exposition of geometric quantization with examples including particles, quantum fields, and bosonic strings, connecting theory with physical concepts.

Findings

Clarifies the geometric quantization process for various physical systems

Demonstrates the application to relativistic particles and string theory

Links geometric quantization to Dirac's axioms of quantization

Abstract

These notes present an introduction to the method of geometric quantization. We discuss the main theorems in a style suitable for a theoretical physicist with an eye towards the physical motivation and the interpretation of the geometric construction as providing a solution to Dirac's axioms of quantization. We provide in detail the examples of free relativistic particles, their corresponding quantum fields, and the bosonic string using formalism of double field theory. Based on lectures written by Gabriel Cardoso.