## The mathematics of Quantum Mechanics

### Prof. Gianfausto Dell'Antonio

This course is divided into three parts, which can be attended separately:

1. Quantization, the Weyl algebra and its representations, second quantization, the wave equation
2. The Trotter-Kato formula, the Feynman-Kac formula: Brownian motion and stochastic processes, Markov semigroups, harmonic semigroups, Gaussian measures
3. Construction of $P_\phi^4$ in two space-time dimension, both with Nelson's and Simon's approach. Euclidean quantum field theory and relation with Wightman axiomatic quantum field theory