## General information

**Description:**In this series of lectures, we discuss quantum many body perturbation theory from a mathematical perspective. The starting point is Feynman diagrams for Gaussian integrals. This only requires the knowledge of freshman calculus. Then assuming basic knowledge of quantum mechanics, we discuss Feynman diagrams for quantum statistical mechanics, and proceed to many body perturbation theory for fermionic systems. If time allows, we will discuss state-of-the-art computational techniques for excited state electrons such as the GW method.

**When:**Thursday 2PM-3:30PM

**Where:**Evans 891

**Prerequisite:**Basic knowledge of quantum mechanics.

In particular, spin, position, momentum, Hamiltonian, Hartree-Fock

These information can be found in the 2016 MSRI-LBNL summer school (Days 1-4). The video of the lectures is available on the MSRI website (2.5 hours each day for 10 days).

Additional reading, matlab codes and projects can be found on the LBNL site.

## Schedule

Date | Content |
---|---|

1/19 | Feynman diagrams for Gaussian integrals. I [Pol sec 1-2] [Eti sec 3] |

1/26 | Feynman diagrams for Gaussian integrals. II [Pol sec 1-2] [Eti sec 3] |

2/2 | Canceled |

2/9 | Quantum statistical mechanics and Feynman diagrams. I. Path integral picture. [Rat sec 1-2] [Fey chap 10] |

2/16 | Quantum statistical mechanics and Feynman diagrams. II. Interaction picture. [Rat sec 1-2] [Fey chap 10] |

2/23 | Second quantization in finite dimensional systems. [Szl] |

3/2 | Canceled |

3/9 | Green's functions for the free Hamiltonian. |

3/16 | Feynman diagrams for fermions. |

3/23 | Field operator and Green's function formalism. GW. |

3/30 | Spring break. |

4/6 | (Michael Lindsey) Large order perturbation theory |

4/13 | (Anil Damle) Topological insulator |

4/20 | (Ze Xu) Density functional perturabtion theory |

## Course materials

**Reading materials**

- [Pol] M. Polyak, Feynman diagrams for pedestrians and mathematicians [.pdf]
- [Eti] P. Etingof, Geometry and Quantum Field Theory [.pdf]
- [Dup] N. Dupuis, Functional integrals [.pdf]
- [MRC] R. Martin, L. Reining and D. Ceperley, Interacting Electrons: Theory and Computational Approaches
- [CGS] E. Cancès, D. Gontier, G. Stoltz, A mathematical analysis of the GW0 method for computing electronic excited energies of molecules
- [Rat] R. Rattazzi, The path integral approach to quantum mechanics [.pdf]
- [Bar] S. Baroni, S. De Gironcoli, A. Dal Corso and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Reviews of Modern Physics 73, 515 (2001)
- [Neg] J. Negele and H. Orland, Quantum Many-particle Systems
- [Fet] A. Fetter and J. Walecka, Quantum Theory of Many-Particle Systems
- [Fey] R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals
- [Szl] S. Szlay et al, Tensor product methods and entanglement optimization for ab initio quantum chemistry, 2015 [.pdf]