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Study recommendation for the focus Gravitational- and Quantum Theory (M.Sc. Physics)

Compulsory Theory of Gravitation Quantum Theory Math./Num. Supplement
1. Term Advanced Quantum Theory (8)
Advanced Laboratory (4)
General Relativity* (8) Particles and Fields (4) Computational Physics III
Advanced Analysis
2. Term Graduate Seminar (4)
Advanced Laboratory (4)
Rel. Astrophysics (4)
Specialization GR
Quantum Field Theory* (8)
Specialization QFT
Math. Methods in Physics
Differential Geometry
3. Term Project preparation Specialization GR Specialization QFT Specialization Math./Num.
4. Term Master’s thesis Specialization GR Specialization QFT Specialization Math./Num.

The lecture and seminar courses during the first two terms are offered each year (credit points in parentheses).
The lecture courses marked with * are essential for the subsequent courses and should be attended.
The QM II course is not a necessary prerequisite for QFT. The latter can already be attended towards the end of the Bachelor studies.

Lectures for Specialization

These lectures are offered every two years. The professors of the TPI will be glad to give individual advice about which courses are useful for your Master’s thesis.

Theory of Gravitation: relativistic astrophysics, cosmology, gravitational waves, numerical relativity, mathematical relativity, magnetohydrodynamics, solitons
Quantum Theory: gauge theories, introduction to particle physics, string theory, lattice field theory, physics of scales, AdS/CFT correspondence, theoretical atomic physics, physics of the quantum vacuum, atoms in external fields
Mathematics/Numerics: spectral methods, symmetries in physics, Lie algebras and Lie groups, mathematical methods in quantum theory, C* algebras, parallel computing, numerics of partial differential equations

Quantum Theory

The Theory of Quantum Fields is of great importance for gaining deeper insight into the fundamental laws of nature and has an increasing impact on novel applications. Quantum fields successfully describe the fundamental interactions in elementary particle physics and are of utmost importance for theories beyond the standard model. At the same time quantum theory plays an increasingly important role in laser-, atomic-, and molecular physics, and is an indispensable tool to study phase transitions in many-body systems.

The professors

Martin Ammon, Stephan Fritzsche, Holger Gies, Andreas Wipf

and their co-workers cover a wide range of research topics of modern quantum theory. The following table links possible research fields with lecture courses offered by members of the research group.

Research Fields Professors Lectures
theory of elementary particles Ammon, Gies, Wipf gauge theories, symmetries in physics
symmetries and phase transitions Ammon, Gies, Wipf physics of scales, lattice field theories
string theory Ammon string theory, AdS/CFT correspondence
(supersymmetric) lattice field theories Wipf lattice field theories, physics of scales
processes in strong electromagnetic fields Fritzsche, Gies physics of the quantum vacuum, atoms in external fields
relativistic atomic physics Fritzsche theoretical atomic physics

Research in quantum theory and quantum field theory profits considerably from mathematical methods and the interdependency of physics and mathematics. Structural insights and rigorous results about quantum systems are often based on advanced mathematical methods taught in specialized lectures on higher analysis, geometry and Lie groups.

Theory of Gravitation

The universal gravitational force dominates on large scales. It is described very successfully by general relativity. Main research areas of the gravity group deal with strong gravitational fields of astrophysical objects like neutron stars and black holes. In many cases the application of general relativity is based on sophisticated numerical methods. In view of the burgeoning field of gravitational wave astronomy with its far reaching implications for astrophysics and cosmology, a deeper knowledge of realistic solutions of the Einstein field equations is urgently needed.

The professors

Bernd Brügmann, Reinhard Meinel

and their co-workers cover a wide range of research topics within mathematical, numerical and astrophysical aspects of gravitational theory. The following table links possible research fields with courses offered by members of the gravity group.

Research Fields Professors Lectures
general relativity Brügmann, Meinel general relativity, mathematical relativity
numerical relativity Brügmann numerical relativity, computational physics, spectral methods
relativistic astrophysics Brügmann, Meinel relativistic astrophysics, magnetohydrodynamics, gravitational waves
alternative theories of gravitation and quantum gravity Ammon numerical relativity, AdS/CFT correspondence

Modern research in general relativity is at the interface of mathematics, numerics and new observational possibilities in astrophysics. Quantizing gravity bridges the gap to quantum field theory. The specialized courses deal with astrophysics and astronomy, mathematical and numerical methods and topics from quantum field theory.


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