Mathematical Physics and Gravity (MAF900)

Content

The course consists of two modules, the obligatory module 1 on differential geometry and one module chosen each year according to the composition of the PhD student body from among module 2 and 3.

Module 1 (5ECTS- FIXED): Differential Geometry

Lie groups / algebras, group effects, subjects from differential geometry (including Differential Forms, orthogonal frames), fiber bundles, tangent bundles, connections.

Module 2 (5ECTS - option1): Supersymmetry:

The module begins with a brief historical and motivational interlude, followed by a review of the necessary mathematical preliminaries including Lie algebras, representations, Lie superalgebras, Clifford algebras, spin groups and spinor representations. The Poincaré (and conformal) algebras will then be introduced as the (conformal) isometry algebras of Minkowski space, followed by their supersymmetric extensions. A brief review of the classification of unitary irreducible representations of the Poincaré group and particle states in field theory will then be given before discussing some concrete examples, together with their associated lagrangians, symmetries and equations of motion. Various supersymmetric extensions of these models will then be presented (in order of increasing complexity) with emphasis on how they realise the Poincaré and conformal superalgebras as supersymmetries. Time permitting, we will then choose from a selection of advanced topics to conclude the module with.

Module 3 (5ECTS - option2): Gravitational waves:

Theory of gravitational waves: The theoretical ideas of what gravitational waves are, how they propagate and how they are produced.

Detection of gravitational waves: The theory of how gravitational waves are detected, and the technology needed to detect them.

Data analysis for gravitational waves: The statistical methods used to find gravitational wave signals in noisy data and the tools used to infer the source properties

Learning outcome

Module 1 (5ECTS- FIXED): Differential Geometry

Manifolds, Lie groups / algebras, group action, subjects from differential geometry (including Differential Forms, orthogonal frames), fiber bundles, tangent bundles, connections.

Module 2 (5ECTS - option1): Supersymmetry:

The module begins with a brief historical and motivational interlude, followed by a review of the necessary mathematical preliminaries including Lie algebras, representations, Lie superalgebras, Clifford algebras, spin groups and spinor representations. The Poincaré (and conformal) algebras will then be introduced as the (conformal) isometry algebras of Minkowski space, followed by their supersymmetric extensions. A brief review of the classification of unitary irreducible representations of the Poincaré group and particle states in field theory will then be given before discussing some concrete examples, together with their associated lagrangians, symmetries and equations of motion. Various supersymmetric extensions of these models will then be presented (in order of increasing complexity) with emphasis on how they realise the Poincaré and conformal superalgebras as supersymmetries. Time permitting, we will then choose from a selection of advanced topics to conclude the module with.

Module 3 (5ECTS - option2): Gravitational waves:

Theory of gravitational waves: The theoretical ideas of what gravitational waves are, how they propagate and how they are produced.

Detection of gravitational waves: The theory of how gravitational waves are detected, and the technology needed to detect them.

Data analysis for gravitational waves: The statistical methods used to find gravitational wave signals in noisy data and the tools used to infer the source properties

Required prerequisite knowledge

Recommended prerequisites

Exam

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Literature