PhD courses offered in English (PP-A)

Particle Physics and Astronomy

Experimental methods in nuclear physics

The aim of the course is to provide an insight in the experimental methods used in contemporary nuclear research. The course intends to discuss all those problems which are of major importance in performing a state-of-the-art experiment in a modern nuclear laboratory.

The discussion starts with the overview of the production of accelerated particle beams and radiation sources. In this chapter the basic properties of the ion-sources, acceleration methods and actual accelerators are explained.

Next we deal with preparation of the targets which are proper for nuclear physics measurements.

The third capitel is the detection of the particles. This huge field of knowledge is organized according to the different basic methods. First the gas-detectors, then the scintillation detectors, the semiconductors and those detectors are discussed which make the orbits of the particles visible. The detection methods of the neutrons are discussed in a separate subcapitel.

The fourth chapter introduces the students in the field of the determination of the cross-sections and goes in details in avoiding typical systematic errors.

At last the course discusses some fields which do not deal directly with the experimental methods, however they are absolutely necessary for an experimentalist working in a laboratory. Now we mention only two of them: radiation protection and organization of the activities in a bigger experimental group in nuclear research.

Completely integrable field theories

  • General equation in the case of weak dispersion and weak non-linearity: Korteweg-deVries equation (KdVE)
  • Other interesting equations: non-linear Shroedinger equation an sine-Gordon equation
  • Scattering theory for the one-dimensional Schroedinger equation
  • Scattering data corresponding to a given potential
  • Reconstruction of the potential from the scattering data: Inverse scattering problem
  • Lax pair for the KdVE
  • Determining of the time dependence of the scattering data for a potential which is solution of th KdVE
  • Using the inverse scattering method for solving the KdVE
  • Multisoliton solutions
  • KdVE as a Hamiltonian system
  • Scattering data as new dynamical variables obtained by canonical transformation
  • Infinite conserved quantities
  • Discrete systems: Toda lattice and Langmuir lattice
  • Inverse scattering method for the discrete systems
  • Generalization of the inverse scattering method for the non-linear Schroedinger equation and the sine-Gordon equation
  • Soliton, multisoliton solutions, soliton-antisoliton scattering and bound states (breather) for the sine-Gordon equation.
  • Generalization of the method

String Theory II.

  • Extension of the bosonic string theory with world sheet fermions in the covariant gauge
  • Supersymmetry of the extended action
  • Superspace description of the action
  • Heuristic introduction of the extende constraints
  • Boundary conditions for the fermion field
  • Neveu-Schwartz and Ramond sectors
  • Quantization of the fermion fields
  • Super Virasoro algebra
  • Spectrum
  • The origin of space-time fermions
  • Critical dimension
  • Superstring in the light cone gauge
  • Lorentz invariance
  • Locally supersymmetric action
  • Derivation of the constraints
  • GSO projection
  • Space-time supersymmetry
  • Type I superstring
  • Closed superstring theories and their spectra:
  • Type IIa and type IIb and heterotic superstring theories.
  • The problem of extra dimensions
  • Connection with supergavity theories
  • Consistence of superstring theories: absence of anomalies

The physics of interstellar dust II.

Semester II: Local deviations from the diffuse dust properties

A few years ago it was still generally believed that the well-studied dust particles in the diffuse interstellar medium are good representatives of cosmic dust in general, perhaps for the whole Universe. Deviations were expected only in a few very special cases, e.g. due to the formation of molecular ice mantles on the surface of grains in dense molecular clouds. In recent years, however, there is strengthening evidence that dust particles and their properties may show significant local deviations from the uniform model. Some examples are the unusually high infrared emissivity measured in high galactic latitude clouds, probably related to an increase of grain size; the variation of the strength and profile of the silicate emission feature around 10?m in different circumstellar disks around young stellar objects; or the discovery of crystalline - rather than amorphous - silicate in some of these disks. In the second part of our course we study these local deviations from the diffuse dust properties.

Perturbation methods in celestial mechanics II.

  • Secular dynamics of small bodies
    • The linear integrable approximation
    • The Kozai integrable approximation
    • Proper elements (asteroid families)
    • Secular resonances
  • Mean motion resonances
    • Simple integrable approximation (phase protection from planetary collision, the 1/1 resonance)
    • Mean motion resonance overlapping (treshold for overlapping in the vicinity of a planet, overlapping of resonances with different planets)
    • Resonant multiplets
  • Three-body resonances
    • Three-body resonant multiplets
    • The asteroid belt
    • The Kuiper belt
    • Chaotic dynamics of the giant planets
  • Secular dynamics inside mean motion resonances
    • Mean motion resonant dynamical system (secondary resonances, the Kozai dynamics, perihelion secular resonances, nodal secular resonances, three-body resonances)
    • The major resonances in the asteroid belt (3/1, 2/1, 3/2)
    • The major resonances in the Kuiper belt (2/3, 1/2)
    • The 1/1 resonance
  • Global dynamical structure of the belt of small bodies
    • Detection of the chaotic zones
    • Chaotic diffusion and macroscopic instability
    • Analytic estimates of Lyapunov time and instability time

Selected Chapters of Hydrodynamics and Magnetohydrodynamics II.


Hydrodynamics, magnetohydrodynamics, kinetic theory and plasma physics are becoming increasingly important tools for astrophysical research. In this lecture we present the fluid mechanics and plasma physics with some astrophysical examples to illustrate the applications of basic principles.

The topics:
  • The scope of HD/MHD, historical background
  • Basic equations
  • Fluids and plasmas in astrophysical context
  • Ideal fluids
  • Viscous fluids
  • Gas dynamics
  • Turbulence and instabilities
  • Basic magnetohydrodynamics
  • Dynamo theory

Our aim is to improve the basic knowledge about the physics of fluids and plasmas with applications to astrophysical systems as illustrations of our theory. Introduction into the methods of scientific works with personal review on previous results, raising new questions and group discussions.

Advanced Informatics in Astronomy


In the last decades, computer facilities are commonly used in every fields of astronomy ranging from observations to numerical modelling. In this lecture we give a short theoretical background of data processing and numerical methods and we present practical knowledges in detail.

The topics:
  • Short introduction into the data processing
  • Manipulation of large amounts of data
  • Direct access to online data bases
  • Basic statistical analysis
  • Typical problems and the properties of equations of fluid dynamics
  • Basic methods of computational techniques for fluid dynamics
  • Programming some numerical schemes through associated astrophysical examples

Our aim is to give assistance on the solution of technical and practical problems, which are occured during the realization of data processing and numerical modelling methods.

Radio Astronomy II

The aim of the lectures in this semester is to show the scientific results that can be achieved by radio astronomy observations, and to put these results in a broader astrophysical context.

Radio galaxies with their energetic clouds of relativistic electrons and cosmic jets extend up to millions of light years into space. A broad variety of atoms and molecules, from neutral hydrogen to complex organic conglomerates can be studied in radio. Quasars, pulsars, masers, the microwave background radiation, gravitational lenses and extra-solar planetary systems were all discovered in radio domain. Historically, radio telescopes have also been used e.g. to detect the relativistic bending of electromagnetic waves which pass near the limb of the Sun, and to measure continental drift on the Earth.

The topics covered in more detail are the following:
  • Classification of celestial radio sources by their emission mechanisms
  • The radio Sun, planetary radio sources, radar observations
  • The Galactic Centre
  • Radio sources in the Milky Way: supernova remnants, pulsars, stars
  • HI and HII regions, molecular clouds
  • Microquasars, radio-loud X-ray binaries, SS 433
  • Extragalactic radio sources: radio galaxies, Fanaroff-Riley classification, unification schemes
  • Compact extragalactic radio sources
  • Active galactic nuclei: quasars, BL Lac objects
  • Relativistic beaming, apparent superluminal motion
  • High-redshift radio galaxies and quasars
  • Cosmological applications
  • The cosmic microwave background radiation
  • The application of VLBI for astrometry and geodesy

Stellar Activity

  • The sun as prototype in the study of stellar magnetic activity
  • sun and stellar spots
  • butterfly diagram
  • Wolf number
  • Maunder minimum
  • spectroscopic activity criteria
  • transition zones and coronae
  • chromospheres in the solar sense
  • Ca II H and K lines
  • Mg II h and k lines
  • timescales of magnetic variability of the sun and stars
  • rotational modulation of activity indicators
  • solar and stellar flares
  • RS CVn stars
  • flare activity of the short period RS CVn star SV Cam
  • direct measurements of the stellar magnetic fields
  • Zeeman effect
  • longitudinal and transverse components
  • Lande factor
  • Babcock's method
  • Robinson's method
  • stellar active regions
  • convection
  • rotation
  • primordial fields
  • Linsky-Haish dividing line
  • Rossby number
  • convective turnover time
  • convection velocity
  • connection between age and activity
  • Mount Wilson H and K project
  • "S" index of stellar activity
  • radiocarbon records of solar activity
  • frequency distribution of magnetic activity in solar type stars
  • Doppler imaging of stellar surfaces

Methods of observational astrophysics

1. Historical overview of observational astrophysics

2. Telescopes and detectors for ground based astrophysics

3-4. Growing importance of observations with space based equipments. Optical, infrared, radio, ultraviolet, X-ray, and gamma ray astronomy with orbiting telescopes

5-6. Distance determination in astronomy based on astrophysical methods and principles

7-8. Basic stellar properties and their determination: spectral type, temperature, mass, radius, magnetic field, and rotation

9. Photometric observations, significance of various photometric systems and extinction/reddening correction

10. Spectroscopic observations, modern multiobject spectrographs. Astrophysical information obtained from the spectral line profile

11. Radial velocity of celestial bodies with reference to the exoplanets and Hubble law

Radio spectroscopy

Aim: a project type introduction to the instrumentation, measurement- techniques and planning, data reduction and evaluation in astrophysical radio spectroscopy.

Tasks for participants:
  • Learn the basic physics of the radiating media/objects and measurement techniques.
  • Get acquainted with the astrophysical use of radio spectroscopic data by reviewing recent journal papers.
  • Get a basic knowledge on the available and planned (esp. European) facilities.
  • Learn the application procedures and prepare to be able to submit a competitive proposal for radio spectroscopy observing time.
  • Learn to use and get practiced in the use of at least one radio spectral line data reduction software package while reducing real measurement data.
  • Evaluate the data-set reduced by the participant.
  • OPTIONAL (depending on available funding)Visit a European facility radio telescope.
Requirements for credit: -
  • Review 1 recent journal article selected (from A&A, ApJ, etc.) by the course leader.
  • Review 1 radio spectroscopy facility instrument
  • Prepare 1 proposal for radio spectroscopy measurement.
  • Reduce a small set of real, radio spectroscopy data (provided by the course leader.
  • Evaluate the reduced data set.

Preliminary (MSc.) studies required in electrodynamics, particle physics, basic astrophysics. Preliminary (MSc) studies in astrophysics - physics of the interstellar medium is not required, but may be very helpful.

Methods of chaos detection

Over the past decades, chaos detection tools and techniques have increasingly (and successfully) been applied to many dynamical systems. Chaos detection tools have thus developed into an active, varied and inherently interdisciplinary field of research. Major advances have been made (e.g.) in the speed and reliability of these techniques. The complexity of chaotic systems makes them a rich source of challenging problems whose analysis often stimulates the development of novel techniques.

The aim of this course is to provide forth and fifth year astronomer and PhD students with an overview of the chaos detection tools. The basic theory behind chaotic systems is explained and algorithms for simulating and characterizing chaotic systems are presented. During the course not only the verbal description of an algorithms are given, but detailed C source codes are worked out for them. Along the course special attention is devoted to programming techniques and style to share the experience I have gained from writing several simulation programs.

Astrostatistics II

  • Data systems, histograms, density models
    • representation of data systems
    • density functions
    • some well known density functions (Gaussian, Laplace, Couchy)
    • fitting a density model to the data system
  • Model-families, supermodels
    • symmetric supermodels
    • asymmetric supermodels
  • Cumulative distributions
    • distribution function: relationship to the density function
    • inverse of the distribution function, Monte Carlo simulations
  • Estimation of the most characteristic value
    • sample median
    • sample mean
    • most frequent value
    • use of density functions
  • Uncertainty within a data system
    • distance of a data system from an x0 value
    • minimum of a norm at the most characteristic value
    • uncertainty of a data system as a minimum of a norm
    • confidence intervals
  • Probability and stochastic variables -axioms of Kolmogorov -stochastic variables (expected value, variance)
  • Multivariate density and distribution function
    • concept of conditional probability
    • Malmquist bias in astronomy
  • Maximum Likelihood estimation
  • Minimalization of I divergence
  • Astronomical examples

Astrostatistics II

  • Nature of the astronomical information
    • multivariate structure of the observed data
  • Basic equation of stellarstatistics
    • density function of the sum of stochastic variables
  • Concept of the characteristic function
    • the central limit-theorem
    • some remarks on the theorem of large numbers
  • Statistical tests
    • A simple test for the mean value
    • tests for distributions (KS test)
  • Concept of covariance and correlation
    • remarks on two-dimensional Gauss distribution
    • test of stochastic independence
    • covariance and correlation matrix
    • partial correlation
    • coefficient of multiple correlation
    • nonlinear dependence
  • Classification of multivarate methods
  • Principal components analysis
  • Factor analysis
  • Discriminant analysis
  • Cluster analysis
    • hierarchical clustering
    • k-means clustering
  • Examples of applying multivariate methods in astronomical problems

Beyond the standard model

The lecture gives an introduction to the basics of beyond the standard model theories.

Topics discussed are:

SU(5) as a prototype of grand unified theories, phenomenology of grand unified theories, dynamical symmetry breaking and the idea of technicolor theories, supersymmetry, phenomenologt of the minimal supersymmetric extention of the standard model, little Higgs models.

Algebraic quantum field theory II.

2nd semester:

  • phase transitions, spontaneous symmetry breaking, the role of infinite degrees of freedom,
  • Hopf algebras, quasitriangular and C^*-Hopf algebras, the Drinfeld double, deformation of Hopf algebras
  • the (braided) rigid monoidal C^*-category of representations of (quasitriangular) C^*-Hopf algebras
  • UHF and AF C^*-algebras, the basic construction
  • classical Ising model and the Ising spin chain,
  • smashed and crossed product by Hopf algebras, Hopf spin chains, algebraic Haag and wedge duality
  • universal coactions and translational covariant field algebras of Hopf spin chains
  • states, GNS-construction, dual algebra of observables
  • phase equivalence of vacuum states, phases of Hopf spin chains
  • ferromagnetic elements in Hopf algebras, ferromagnetic states in Hopf spin chains
  • causal dynamics, unitary implementations of causal dynamics

Solitons and instantons II.

  • The principles of soliton quantization.
  • The quantization of the kink solution.
  • The kink mass and its renormalization.
  • How to handle the translation mode.
  • Axiomatic approach and the role of the classical solution.
  • Equal time commutators in the axiomatic framework.
  • Collective coordinates in scalar field theories.
  • Quantization of collective coordinates.
  • The dilute instanton gas for periodic potential.
  • Null modes in functional integrals.
  • The topological vacua of 1+1 dimensional Abelian Higgs model.
  • Vacuum tunneling in the 1+1 dimensional Abelian Higgs model.
  • Modular dynamics.

The algebraic Bethe Ansatz and its applications

The aim of this series of lectures is to give a flavour for some of the main ideas and techniques underlying two-dimensional integrable systems of the statistical physics and field-theory.

  • 2D vertex models: vertex operator, monodromy matrix, transfer matrix
  • The 6-vertex model
  • Integrability of vertex models and the Yang-Baxter equation (YBE)
  • Solution os the YBE yielding the 6-vertex model
  • Connection of 2D vertex models and 1D quantum systems: the 6-vertex model and the anisotropic Heisenberg chain
  • The algebraic Bethe Ansatz (ABA) for the 6-vertex model
  • The application of the ABA for the 1D spin ½ δ-Fermi gas
  • Spin chains with S≥1

Inflationary Cosmology

  • Einstein's equations of gravitation.
  • Kinetic Boltzmann equation of realtivistic matter.
  • Inflation.
  • Linear theory of cosmological perturbations.
  • Evolution of the dark matter.
  • Cosmological microwave background radiation.

Finite Temperature Quantum Fields

  • Quantum fields in thermal equilibrium.
  • Phase transitions in quantum field theory.
  • Thermodynamics of the N-component scalar field and its application to the QCD phase transformation.
  • Time evolution of quantum fields near thermal equilibrium.
  • Review of the inflationary period of the Universe.
  • Field theory of the cosmological reheating.