Minicourse on "Methods of quantization"

By Elisa Ercolessi (U. Bologna)

We recommend the pre-course Preliminaries on Quantization on September 1 & 2 to new researchers on the topic.

Methods of quantization (3 hours)

This course aims at giving an introduction to some modern methods of quantization. More specifically we will deal with:

  1. Weyl quantization on phase space: exponential form of canonical commutation relations, properties of Weyl operators, Moyal product.
  2. Coherent States and Bargmann-Fock representation: properties of coherent states, Fock basis, the complex phase space representation;
  3. Feynmann’s Path Integral: Green kernel of the Schroedinger operator, path integral approach in phase space, in coordinate space, in coherent space representation.

Throughout the three lectures, the free particle, the harmonic oscillator and the two-level system will be used as guide examples to see the main principles in action.