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General


Description

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.

Semester

Autumn 2019 (Monday, October 7 to Friday, December 13)

Hours

  • Live lecture hours: 10
  • Recorded lecture hours: 0
  • Total advised study hours: 40

Timetable

  • Mon 13:05 - 13:55

Prerequisites

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.

Syllabus

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

Other courses that you may be interested in:

Bibliography


No bibliography has been specified for this course.

Assessment



The course will be assessed by an öpen book" take-home exam. Questions will be roughly of the type given as exercises in the individual chapters of the lecture notes. The pass mark for the exam is 50%.

No assignments have been set for this course.

Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
advqt-notes.pdf


Recorded Lectures


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