Michele Schiavina: Catalogue data in Spring Semester 2021

Name Dr. Michele Schiavina
Address
Dep. Mathematik
ETH Zürich, HG F 27.4
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 34 67
E-mailmichele.schiavina@math.ethz.ch
DepartmentPhysics
RelationshipLecturer

NumberTitleECTSHoursLecturers
401-4816-21LMathematical Aspects of Classical and Quantum Field Theory8 credits4VM. Schiavina, University lecturers
AbstractThe 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.
ObjectiveThe 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.
ContentAbstract (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.