VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.
Mathematical Aspects of Classical and Quantum Field Theory
Last Updated: 2026-02-05 15:54:14
Abstract
The course will cover foundational topics in classical and quantum field theory from a mathematical standpoint.Starting from the example of classical mechanics, the relevant mathematical foundations that are necessary for a rigorous approach to field theory will be provided.
Objective
The objective of this course is to expose master and graduate students in mathematics and physics to the mathematical foundations of classical and quantum field theory. The course will provide a solid mathematical foundation to essential topics in classical and quantum field theories, both useful to mathematics master and graduate students with an interest but no previous background in QFT, as well as for physics master and graduate students who want to focus on more formal aspects of field theory.
Content
Abstract (long version) The course will cover foundational topics in classical and quantum field theory from a mathematical standpoint. Starting from the example of classical mechanics, the relevant mathematical foundations that are necessary for a rigorous approach to field theory will be provided. The course will feature relevant instances of field theories and sigma models, and it will provide a first introduction the the concepts of quantisation, from mechanics to field theory. Using scalar field theory and quantum electrodynamics as guideline, the course will present an overview of quantum field theory, focusing on its more mathematical aspects, including, if time permits, a modern approach to gauge theories and the renormalisation group. Content The course will start with an overview of geometric concepts that will be used throughout, such as graded differential geometry, as well as fiber and vector bundles. After brief review of classical mechanics, interpreted as a first example of a field theory, a thorough discussion of classical, local, Lagrangian field theory will follow, covering topics such as Noether’s Theorems, local and global symmetries. We will then present and discuss a number of examples from gauge theory. In the second part of the course, quantisation will be discussed. The main examples of the scalar field and electrodynamics will be used as a guideline for more general considerations on the quantisation of more general and involved field theories. In the last part of the course, we plan the discussion of modern approaches to quantisation of field theories with symmetries, renormalisation, and of the open challenges that arise.
General Information
- Language
- English
- Levels
- DR , MSC
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Mathematical Aspects of Classical and Quantum Field Theory
**together with University of Zurich**
|
|
4 h weekly |
Offered In
-
-
Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
-
-
-
-
-
Doctoral Department of Mathematics (More Information at: The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM. WARNING: Do not mistake ECTS credits for credit points for doctoral studies!)
-
Graduate School (Official website of the Zurich Graduate School in Mathematics:)
-