Advanced Graduate Lecture Course:
Lecture Course (260053 VO): January 10 to 29, 2018
Time: 9:15 - 10:45 a.m
Wednesday, January 10, 2018Further Dates:
Friday, January 12, 2018, Friday January 19, 2018, Wednesday, January 24, 2018, Friday, January 26, 2018
Monday, January 29, 2018
In the he first part of the course I give an extensive introduction into the frame-independent formulation of Newtonian Gravity developed by Elie Cartan, the so-called Newton-Cartan Gravity. Examples from General relativity are used to explain the construction of this Newton-Cartan formulation.
In the second part of the course I will discuss three more specialistic topics: (i) Non-relativistic limits, (ii) Non-relativistic supersymmetry and (iii) Applications to a concrete model: the Quantum Hall Effect.
Content of the course:
- Lecture 1: an overview of those aspects of General Relativity that are relevant for the remaining part of the course
- Lecture 2: The kinematics of General Relativity will be derived by applying the gauging technique to the Poincare algebra
- Lecture 3: The gauging technique will be applied to construct the kinematics of Newton-Cartan Gravity
- Lecture 4: Different non-relativistic limits are discussed that relate relativistic gravity or matter theories to non-relativistic ones.
- Lecture 5: An introduction to non-relativistic supersymmetry will be given with an emphasis on supersymmetry in a curved background in view of applications of the so-called Supersymmetric Localization technique.
- Lecture 6: The Newton-Cartan formalism will be applied to the concrete example of the The Quantum Hall Effect
Aims for the course:
- Understanding the Newton-Cartan Formalism
- understanding relating relativistic gravity and matter theories to non-relativistic ones by taking limits
- being able to work with non-relativistic supersymmetry
- being able to apply the Newton-Cartan formalism to a concrete example: the Quantum Hall Effect
Link to the course directory
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