## Two Lectures on Path Integral, Feynman Diagrams and its Application to SYK Model

**Speaker(s): ** Pengfei Zhang（Tsinghua University）

**Time: ** 19:00-21:00 April 2, 2019 - April 3, 2019

**Venue: ** Room 77201, Jingchunyuan 78, BICMR

In the first pedagogical talk, I would give a quick introduction to the quantum field theory in condensed matter physics. I would firstly derive the path-integral representation of partition function for many-body systems. In such formulism, one could efficiently perform perturbation theory to calculate correlation functions using Feynman diagrams. Here, I will use the perturbative expansion of weakly interacting fermions as an example (may also cover the BCS problem depending on time.). I would also explain why we care about correlation functions in condensed matter physics.

In the second talk, I would use the path integral approach to study the SYK model. By analyzing the large-N structure, we will select the diagrams that contributes to the leading order of 1/N, which shows the conformal symmetry of the low-energy limit. Based on the result of two-point correlation function in the conformal limit , I will show the Lyapunov exponent is 2pi/beta. Finally I will discuss the derivation of the effective action of the system and talk about its relation to the AdS2 dilation gravity.