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Mathematical Physics and Gravity MAF900

The course gives an introduction to a selection of modern topics in mathematical physics, gravity and supersymmetry. 


Course description for study year 2022-2023. Please note that changes may occur.

Facts
Course code

MAF900

Version

1

Credits (ECTS)

10

Semester tution start

Spring, Autumn

Number of semesters

1

Exam semester

Spring, Autumn

Language of instruction

English

Content

Course 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

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

Required prerequisite knowledge
None
Recommended prerequisites
FYS500 Analytical Mechanics and Field Theory
Exam
Form of assessment Weight Duration Marks Aid
Oral exam 1/1 Passed / Not Passed None permitted

Course teacher(s)
Course coordinator: Sigbjørn Hervik
Course teacher: Eirik Eik Svanes
Course teacher: Alex Bentley Nielsen
Head of Department: Bjørn Henrik Auestad
Method of work
Lectures, seminars, guided reading
Open for
Computer Engineering - PhD Technology and Natural Science - PhD programme
Course assessment
Form and/or discussion according to established guidelines.
Literature
Search for literature in Leganto