Research video based on arxiv.org/abs/1505.04809, published in J. Math. Phys. 57, 092301 (2016).

Outline:
0:33 - statement of the problem
1:10 - problematic example from Peskin-Schroeder
2:11 - Wiener measure
2:22 - unreasonable effectiveness of path integral methods
3:02 - Feynman diagrams
3:30 - Wick rule
4:54 - formal series expansion
5:31 - Wick expansion
6:04 - example of the Wick expansion
7:20 - formal change of variables
9:02 - how to understand path integrals
10:08 - summary of paper's achievements
11:03 - stationary phase/steepest descent
11:26 - conclusion and future outlook