Mathematical Foundations of Second Quantization
Winter Semester 2025/26, FAU

Abstract. This course provides a rigorous introduction to the mathematical formalism of second quantization, the framework underlying quantum field theories and many–body physics. We begin with a review of key results on self–adjoint operators, including the Kato–Rellich theorem. The quantum harmonic oscillator is revisited as a guiding example, leading naturally to the construction of Fock spaces. From there, we develop the general theory of bosonic and fermionic Fock spaces, introduce creation and annihilation operators, and explore the second quantization of single–particle operators. We will finally use this knowledge to introduce models of light–matter interaction, such as the spin–boson model.

The course is self–contained and is intended for students with a background in quantum mechanics and an interest in deepening their understanding of the mathematical tools that support quantum many–body and field theories.

Schedule (unless otherwise specified):

• Main lectures: TBA.

• Exercise classes: TBA.

Main reference: TBA.

Slides: TBA.

Solutions of exercises: TBA.

Diary of the lectures

• TBA.