In this talk I plan to show the importance of Noncommutative Geometry to mathematically describe quantum motions in Quantum Field Theory. At the first step, I explain the construction of a new class of spectral triples with respect to the information of Dyson--Schwinger equations. At the second step, I explain the structure of a new noncommutative differential geometry machinery derived from the BPHZ renormalization of Dyson--Schwinger equations.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/5312