MAGIC101: Advanced Quantum Theory

The aim of this module is to extend knowledge of quantum mechanics from undergraduate courses by emphasizing its overall mathematical structure, as well as its applications to a wide range of topics in mathematical physics.

We will introduce an abstract framework for quantum theory, based on tools from the theory of operator algebras, which is general enough to describe all its subareas: quantum mechanics, quantum statistical mechanics (including thermodynamics in infinite volume), quantum field theory on Minkowski space and on curved spacetimes, as well as including classical probability theory as a special case.

Students should have attended either a first course in quantum mechanics, or have some knowledge of operator theory (on infinite dimensional Hilbert spaces); ideally both, but participants with experience in either area are welcome.
For some lectures, familiarity with other topics in Theoretical/Mathematical Physics will be helpful, such as Genera Relativity / differential geometry.

The presentation style is expository, i.e., each lecture will give an overview of a subject area, rather than working out the technical details.

A tentative list of topics is:

Probability theory
Basics of quantum theory
Algebras, states, GNS representation
Thermodynamics and the KMS condition
Free quantum fields on Minkowski space
Linear quantum fields on curved spacetimes
Frameworks for interacting quantum field theories

MAGIC101: Advanced Quantum Theory

Course details

Semester

Hours

Timetable

Description

Prerequisites

Syllabus

Lecturer

Dr Henning Bostelmann

Bibliography

Assessment

Files

Lectures