Ma 192 a: Geometry and Arithmetic of Quantum Fields

Fall 2008, Caltech Math Department, Tuesday-Thursday 2:30-3:55 pm, 151 SLN; Instructor: Matilde Marcolli

* The book "Feynman Motives" based on the lectures of this course will soon appear published by World Scientific

Brief Course Description

The course will focus on mathematical structures of renormalization in perturbative quantum field theory and of the standard model of elementary particle physics. The main themes will be the mysterious relation between renormalization in quantum field theory and the theory of motives in arithmetic geometry, as well as the models of particle physics obtained using noncommutative geometry.

List of Topics


Lecture notes of the course will be posted here


Students taking the class for credit will be required to contribute either a written essay on a topic related to the material of the class (to be agreed upon with the instructor) or an oral presentation in the Research Seminar (see below). Please contact the instructor at your earliest convenience to schedule a time for a presentation and to decide the topic of presentation/essay.

Research Seminar

The course will be accompanied by a Research Seminar: the seminar meets once per week, alternating between Thursday 4:15-5:15 pm and Tuesday 5:30-6:30 pm.

The first seminar will be on Thursday October 16 at 4:15 pm.

Titles and abstracts of seminars will be posted here.

Suggested reading material for seminar presentations

More references will be added later on. Other choices for seminar presentations will be made available during the class.


The class will follow roughly the first chapter of the book: Additional reading material used in the class will be listed below.

Useful General Bibliographical References

  • Quantum Field Theory:
  • An introductory reading: More detailed books on QFT:
  • Affine group schemes and commutative Hopf algebras:
  • Renormalization:
  • Motives:
  • Particle physics: Noncommutative Geometry: More references will be added later on.

    back to my home page