MAGIC101: Advanced Quantum Theory

Course details

Semester

Spring 2021
Monday, January 25th to Friday, March 19th; Monday, April 26th to Friday, May 7th

Hours

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

Timetable

Fridays
13:05 - 13:55

Course forum

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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. 

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 

Lecturer

  • HB

    Dr Henning Bostelmann

    University
    University of York

Bibliography

No bibliography has been specified for this course.

Assessment

Description

The course will be assessed by a single take-home exam. You will need to achieve 50% to pass.

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Lectures

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