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Courses Compulsory for Masters of Science in Physics
Philosophical Problems of Natural Science (5th year students, 36 hours)
The world’s physical picture as an integral image of nature. Classical and non-classical physics
described on micro- and macro-levels. Event space and object models (a corpuscle and
continuum) in classical physics. Substance and electromagnetic radiation as matter forms. Mass,
momentum, energy and angular momentum as fundamental characteristics of the objects.
Conservation laws and their relation to space-time properties. A deterministic and stochastic
description of the motion. Ideas of reductionism and independence of the description on microand macro-levels. Modern interpretation of the notions and elements of classical
thermodynamics. The space-time and matter interconnection idea in General relativity. The
fundamental constants – Planck’s and Bolzmann’s constants. Relativity of boundaries between
micro- and macro-descriptions of physical systems. The integrity problem in a non-classical
description of nature in physics. Principles of constructing the world’s integral multidimensional
physical picture. Evolution and self-organization concepts in nature. Validity limits of the
modern physical theories.
English Language (5th and 6th year students, 106 hours)
The usage of tenses. Passive Voice. Subjunctive Mood. Gerund. Scientific terms and their
usage. Practice in translating texts and writing abstracts of articles and books in physics. Reading
and retelling socio-political texts. Oral practice.
History and Methodology of Physics (5th year students, 36 hours)
Prehistory of physics. Beginning of physics. Classical physics. Comtemporary physics.
Newton's mechanics. Time and space. Analitical mechanics of Lagrange and Hamilton, and
Hamilton-Yacobi. Statistical mechanics. The range of validity of the classical mechanics. Origin
of knoledges on electricity and magnetizm. The law of Coulomb. Electric current.
Electromagnetic field. Faraday. Electromagnetic induction. Electrodynamics of Maxwell.
Electrodynamics of continious media. Geometrical optics. Fermat's principle. Dispersion and
difraction of light. Newton's corpuscular concept of light. Wave concept of light. Eather and
experiments. Transformations of Lorentz. Relativity. Relativistic mechanics. Thermogen of
Plato. Kinetic nature of the heat. Thermodynamics {Clausius, Thomson-Kalvin, Onsager,
Prigogine). Statistical physics. Kinetic theory. Irreversibility problem. The concept of atom.
Discovery of electron, X-rays. Planck's quanta. The light quanta. Bohr's atom. Arising of
quantum mechanics. The modern concepts on atom. Elementary particles. Universe. Gravity.
Computer Technology in Science and Education (5th and 6th year students, 106 hours)
Computer technologies in physical researches: mathematical calculations, numerical
simulations, control of experiments, virtual device design, distant education. Most popular OS.
Introduction to Web-design. What is HTML. Syntax and main elements of HTML. Objects and
forms. Style tables, lists, scenarios. Methods of hypertext formation. HTML file formats. Webgraphics. Design principles for electronic textbooks. Introduction to programming languages.
Programming at low level. C, Pascal, Fortran; their realization on different platforms. Program
libraries. Software for mathematical calculations. Visualization of calculation results.
Current Problems of Physics, Fundamental Constants (5th year students, 12 hours)
Advances in the theory of unification of interactions with gravitation, multidimensional models,
main exact solutions in cosmology and spherical symmetry cases and their role in solving basic
problems of cosmology and localized objects, dark energy and dark matter problems in approach
with extra dimensions, cosmological models with phantom matter, possible variations of
fundamental physical constants (FPC), cosmological models with variations of the gravitational
constant G, transition to new definitions of SI units, based on FPC, present state and existing
problems.
Teaching Physics (5th year students, 12 hours)
Physics as a subject. Research and training methods. Equipment of training process in physics.
Methods of laboratory practice conducting. Forms of university examining. Computers in
training. Organization forms of studies. Individual work. Methodical and methodological
problems in studying various sections of physics. Practical studies conducting. Establishing of
new laboratory studies and lecture tests. Lecture abstracts preparing.
Advanced Theoretical Physics (5th and 6th year students, 72 hours)
Advanced analytical mechanics, hydrogasdynamics, special relativity, microscopic and
continuum electrodynamics, nonrelativistic and relativistic quantum mechanics intended for
astronomical applications (celestial mechanics, relativistic astrophysics, quantum cosmology
etc.).
Courses for Choice
Introduction to Classical Field Theory (5th year students, 36 hours)
Fundamental fields (scalar, spinor and vector ones). Klein-Gordon, Dirac, Maxwell equations.
Lagrangian choice criteria. Conservation laws (Noether theorem). Global and local gauge
invariance. Interacting fields. Abelian and non-Abelian gauge fields. Yang-Mills field.
Topical Problems in Energetics and Ecology (5th year students, 24 hours)
Evolution of human society and development of energy release methods. Estimation of world
reserves for non-regenerating sources of energy. Alternative sources of energy. Foundations of
nuclear energetics. Fission and synthesis of atomic nuclei. Problem of waste products
conservation in nuclear energetics. Energetics and ecology
Courses Compulsory for Specialization ”Gravitation, Cosmology and
Relativistic Astrophysics”
General Astronomy (5th year students, 36 hours)
Spherical astronomy (coordinates, time measurement). Solar system (the Sun, planets, satellites).
The Galaxy (structure, motion of stars). Stars (structure, spectrum, luminosity). Extragalactic
astronomy (types of galaxies, their spatial distribution, active galaxy nuclei). Elements of
cosmology (Copernican principle, a hot Universe’s model).
Physical Kinetics (5th year students, 36 hours)
Part I. Kinetic theory. The object and general notions of kinetic theory. Statistical ensemble.
Bogoliubov’s chain of equations. Boltzmann’s equation. Kirkwood multi-scales method.
Boltzmann H-theorem. Enskog – Chapman method. Kinetic equations for plasma. Landau’s
damping.
Part II. Brownian motion and diffusion. Fokker – Planck equation. Markov chains.
Smoluchowski equation. Langevin equations. Complex diffusion. Two-phase medium with
random internal geometry.
Part III. Non-equilibrium thermodynamics. Foundations of non-equilibrium thermodynamics.
Transport equations and conservation laws. Entropy for non-equilibrium systems. Linear
Onsager relations.
Quantum Field Theory (5th year students, 48 hours)
Part I. Relativistic description of particles. Foundations of classical field theory. Variational
principle. Structure of conserved quantities. Classical “displacement”, “rotation”, and “charge”
theorems in Hamiltonian formalism. Methods of group theory in physics of particles.
Infinitesimal method for constructing irreducible representations of Lie groups. Irreducible
representations of rotation group, Lorentz group, and Poincaré group. The Dirac’s equation.
Internal symmetry groups. Dynkin schemes and root diagrams. Principle of gauge symmetry.
Higgs effect. Supersymmetry.
Part II. Theory of quantum fields. Dirac quantization rule. Canonical commutation relations. The
second quantization method. Von Neumann’s theory of infinite tensor products of Hilbert
spaces. Fock space. Foundations of generalized functions theory. Schwarz space and functionals
in it. Tensor representation of operators in Fock space. Superselection rule. General principles of
fields quantization. Schwinger – Feynman dynamical principle. Quantization of scalar field,
massive vector field, and electromagnetic field. Quantization of spinor field. Scattering matrix in
quantum field theory. Tomonaga – Schwinger equation and Dyson’s solution. S-matrix
properties. Feynman’s rules in quantum electrodynamics. Calculation of the simplest effects.
Estimation of radiation corrections. Heisenberg theorem on renormalizable field theories.
Bogoliubov’s R-operation and elimination of divergences. Dyson and Schwinger equations for
complete Green functions. Bethe – Salpeter equation. Axiomatic theory of S-matrix.
Classical Gravity Theory (5th year students, 36 hours)
Riemannian geometry and tensor analysis (metric, geodesics, covariant derivative, curvature
tensor). Gravitation field equations. Energy-momentum tensor. Exact solutions to HilbertEinstein’s equations (Schwarzschild and Friedmann equations). Classical effects of general
relativity (perihelion shift, relativistic deflection of light, gravitational red shift).
Theory of Nuclei and Particles (5th year students, 96 hours)
Part I. Foundations of nuclei theory. Types of particles and nuclei interactions. Main properties
of nuclei. Nuclei models. The origin of nuclear forces. Deuteron. Nuclear reactions. Decays of
nuclei. Charge symmetry of strong interactions.
Part II. Relativistic theory of particles scattering. The Dirac’s equation. Spin in Dirac theory.
Polarization density matrix. Relativistic theory of quantum transitions. Feynman diagrams.
Decay probabilities and effective sections of scattering. Methods for calculating matrix elements.
Cartan’s mapping. Relativistic theory of scattering. Mott and Rosenbluth formulae.Pions
scattering. Scattering of polarized electrons. Scattering by nuclei.
Part III. Classification of particles. Historical introduction. Group theory approach to particles
classification. Unitary groups. Masses relations. Spin effects estimation in quark models.
Supersymmetry.
Part IV. Weak interaction. Pauli hypothesis on neutrino. Fermi theory of beta-decays. Structure
of matrix elements. Fermi and Gamov – Teller selection rules. Five variants of weak interaction.
Neutrino physics. Lepton numbers. Neutrino mass and neutrinos oscillations. Neutrino in
astrophysics.
Introduction to the Theory of Electro-Weak Interactions (6th year students, 24 h)
Part I. Current – current theory of weak interactions. Weinberg’s classification of currents.
Conservation of vector current and partial conservation of axial-vector current. Fermi theory of
beta-decay. General form of current – current Lagrangian of weak interaction. Creation of V-A
theory of beta-decay and its generalization to other processes. Weak form-factors. Nonrenormalizability of theory with intermediate vector boson.
Part II. Gauge models. Principle of gauge invariance. Local SU(2)-symmetry. Yang – Mills
fields. T’Hooft – Polyakov monopole. Asymptotic freedom. Spontaneous symmetry breaking.
Higgs fields and Goldstone theorem. Weinberg – Salam model of unitary electro-weak
interaction. Intermediate vector bosons. Main principles of quantum chromodynamics. Grand
unification of interactions. Supersymmetry.
Mathematical Methods in Gravity Theory (5th year students, 24 hours)
Elements of the analysis on normalized spaces (sets and manifolds, Frechet’s derivative).
Smooth manifolds (charts and atlases, category notion). Tangent spaces (differential, vector
field). Exterior forms.
Foundations of Quantum Chromodynamics and String Theory (5th and 6th year students,
48 hours)
Part I. Foundations of quantum chromodynamics. Foundations of gauge fields theory, Yang –
Mills fields. Color symmetry group SU(3) as gauge group. Quantum theory of gauge fields.
Schwinger currents method. Faddeev – Popov trick. Ghost fields. Renormalization group
equations. Consequences of quantum chromodynamics. Problem of quark (color) confinement.
Deep inelastic scattering of electrons by nucleons. Lattice variant of quantum chromodynamics.
Quark – gluon plasma. Low-energy approximation in quantum chromodynamics. Nambu – JonaLasinio superconducting model. Skyrme chiral model.
Part II. Foundations of strings theory. Introduction into strings theory. Regge high-energy
asymptotic for scattering amplitude and its explanation in rotating string theory. Quantum
anomalies. Fudzikawa’s method of calculating the Abelian anomaly. Chern characteristic
classes. Katz – Moody algebras. Nambu – Goto bosonic string. Virasoro algebra. Ramon –
Neveu – Schwarz spin string. Virasoro super-algebra. Tachyon vacuum. Green – Schwarz
superstring. Types of excitations for closed string. Compensation of anomalies principle. Dual
properties of superstrings. Polyakov’s string. Compactification of extra dimensions problem.
Multidimensional Models in Gravity Theory (6th year students, 36 hours)
Smooth manifolds with a metric (metric, covariant derivative, curvature tensor, geodesic
equations). Multidimensional cosmological models (multidimensional generalizations of Kasner
and de Sitter solutions, accelerated expansion of the Universe and gravitational constant
variation) Models with branes (form fields, scalar fields, supergravity).
Relativistic Astrophysics and Cosmology (5th and 6th year students, 48 hours)
Theory of radiative transfer in stellar atmospheres. Gaseous nebulae. Background radiations.
Final stages of stellar evolution. Extragalactic astronomy. Gravitational waves. Cosmological
models. Observational cosmology. Cosmological scenarios. Physical cosmology. Anisotropic
cosmological models. Rotation origin problem in astronomy.
Quantum Gravity (5th and 6th year students, 48 hours)
Classification of gravity quantization approaches (Zel’manov’s cube). Quantum mechanics of a
charge in a centrally symmetric gravitational field (a nonrelativistic case taking account of
DeWitt’s force). Electromagnetic and gravitational radiations of graviatoms. Quantum
geometrodynamics (Wheeler-DeWitt’s equation). Quantum cosmology (The Universe’s birth as
a tunnelling). Quantum field theory in curved space-time (Hawking and Unruh effects, particle
creation in the early Universe).
Courses for Choice
Black Hole and Wormhole Physics (5th year students, 12 hours)
Static spherical symmetry. Kruskal’s metric. Carter-Penrose’s diagrams. Scalar-tensor theory.
Horizons, singularities and wormholes. No hair and no-go theorems. Phantom fields and regular
configurations. Regular black holes.
Stellar Evolution, Galaxy Dynamics, Interstellar Medium Physics (5th year students,
12 hours)
Interstellar medium (cloudy structure, Stroemgren zones, gravitational instability). Protostars
(Jeans’ length and mass, fragmentation while expanding, protostar tracks). Stellar equilibrium
(hydrostatic and energy ones, Emden’s equation, dependence of the luminosity on the mass, the
temperature at the star centre). Stellar dynamics (orbits of stars in the Galaxy, statistical
distribution of stars, rotational curves, spiral structure).
Cosmic Electrogasdynamics (6th year students, 12 hours)
Electrogasdynamical processes in astrophysics (shocks in supernovae explosions, solar flares,
cosmic ray acceleration, accretion onto compact astrophysical objects). Magnetohydrodynamics
(magnetic field line freezing-in, forceless field). Waves in the plasma (Alfvén, acoustic,
magnetoacoustic ones, plasma oscillations).
Algebra and Geometry of Space-Time (6th year students, 12 hours)
Spinor and twistor structures (spinors and null vectors, field equations in the spinor formalism).
Quaterniona and physical geometry (biquaternionic relativity, relation of quaternions to
twistors). Quaternionic analysis and algebrodynamics (a complex eikonal equation, particles as
quaternionic field singularities). Complex space-time concept (complex space-time and quantum
uncertainty).
Structure of Elementary Particles (5th year students, 60 hours)
Composite models of particles. The simplest models of atomic nuclei. Nuclear form-factors.
Phenomenological description of elementary particles structure. Mott and Rosenbluth formulae.
Hofstadter experiments on determination of proton structure. Nonlinear models in physics of
fields and particles. Composite models, quarks, gluons. Color. Grand unification.
Introduction to Quark Theory (5th year students, 24 hours)
First composite models of particles. Symmetry between leptons and quarks. Lie algebras and
groups. Unitary symmetries. Quark constituents in hadrons. Masses relations. Parton model.
Color. Weinberg – Salam model of electroweak interaction of leptons. Foundations of quantum
chromodynamics. Problem of quarks confinement.