Summer Term 2024

1300172103
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Content

* Manifolds
* Geodetics, curvature, Einstein-Hilbert action
* Einstein equations
* Cosmology
* Differential forms in General Relativity
* The Schwarzschild solution
* Schwarzschild black holes
* More on black holes (Penrose diagrams, charged and rotating black holes)
* Unruh effect and hawking radiation

Goal

After completing the course the students * have a thorough knowledge and understanding of Einstein's theory of General Relativity including the necessary tools from differential geometry and applications such as black holes, gravitational radiation and cosmology,  * have acquired the necessary mathematical tools from differential geometry, are trained in their application to physical situations with strong gravity and are familiar with their interpretation, * have advanced competence in the fields of theoretical physics covered by this course, i.e. the ability to analyze physical phenomena using the acquired concepts and techniques, to formulate models and find solutions to specific problems, and to interpret the solutions physically and communicate them efficiently, * are able to broaden their knowledge and competence in this field of theoretical physics on their own by a systematical study of the literature.

1300172206
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Content

The course will cover advanced topics in Cosmology concerning booth theoretical and observational aspects. Further information on "Uebungen":

https://uebungen.physik.uni-heidelberg.de/vorlesung/20241/1836

1300172209
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Course Information

Content

The lectures are Mondays and Wednesdays at 2:00pm at großer Hörsaal, Philosophenweg 12

Motivation:

Nonlinear dynamics is an interdisciplinary part of mathematical physics, with applications in such diverse fields as mechanics, optics, chemistry, biology, ecology, to name but a few. Equations with nonlinearities show a much more diverse behavior than their linear counterparts, for instance self-sustained oscillations, nonlinear competition (as linear superposition does not hold anymore), chaotic dynamics and pattern formation. Pattern formation, in turn, is one of the most fascinating and intriguing phenomena in nature: it takes place in a wide variety of physical, chemical and biological systems and on very different spatial and temporal scales: examples are convection phenomena in geosciences and meteorology, but also patterns occurring in chemical reactions and bacterial colonies. In some circumstances, pattern formation is undesired, for instance the formation of spiral waves leading to cardiac arrhythmias in the heart muscle. In other contexts, pattern formation is even essential for the functioning of a system as in cell division and embryo development.

Goal

Contents: The lecture will start with an introduction to nonlinear dynamics on the level of ordinary differential equations (ODEs), introducing concepts like phase space analysis, attractors, (in)stability of solutions and bifurcations, as well as nonlinear oscillations.  We will then proceed to study spatio-temporal behavior, i.e. partial differential equations (PDEs) and discuss the main questions in pattern formation: when will a homogeneous state become structured, i.e. unstable towards a pattern? What are the generic scenarios/types of patterns? When are patterns stable and are they unique? What determines the wavelength / period in time / amplitude of a pattern? Importantly, a universal description of pattern dynamics exists, that is independent of the system-specific pattern formation mechanism. The method to obtain this description is called multiple-scale reduction, resulting in an amplitude equation (also called center manifold), which is nothing but the famous Ginzburg-Landau equation (Nobel Prize in Physics 2003, originally derived for superconductivity).  Finally, nonlinear waves and solitons (localized waves) will be discussed. They again occur in many systems, from coupled nonlinear springs to hydrodynamic surface waves and nonlinear optics. In addition, solitons have intriguing mathematical properties that will also be discussed.

1300172215
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Course Information

Content

The lecture course provides an introduction to the strongly-correlated physics of QCD and Quantum Gravity. The related physics problems are treated within the Functional Renormalisation Group (fRG), and a survey of alternative approaches is provided.

    Outline

    I The Functional RG
        Euclidean QFT 
        Functional Renormalisation Group
        Critical Phenomena & Fixed Points 

   II  QCD
        Introduction 
        Non-Abelian gauge theories & confinement 
        Chiral symmetry breaking in QCD 
        QCD at finite T 
        A glimpse at the QCD phase diagram 

  III Quantum Gravity
        Introduction 
        RG approach to quantum gravity 
        Gravity and matter 
        Cosmological applications*

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Content

In Ergänzung zur Vorlesung sollen fortgeschrittenere oder aus Zeitgründen nicht besprochene Themen aus der Elektrodynamik behandelt werden.

Goal

Vertiefung der Kenntnisse der Elektrodynamik, Erlernen des wissenschaftlichen Vortragens und der wissenschaftlichen Diskussion.

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1300172221
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1300172223
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