Download PROGRAMY STUDIÓW II STOPNIA

PROGRAMY STUDIÓW II STOPNIA
Przedmioty wymienione są alfabetycznie w kolejności zgodnej z planami studiów
FIZYKA TEORETYCZNA
Przedmioty wymienione są alfabetycznie w kolejności zgodnej z polskimi nazwami w planie
studiów
Przedmiot Elementy astronomii i astrofizyki został opisany przy studiach I stopnia a
przedmiot Kultura-historia-globalizacja przy specjalności Fizyka doświadczalna na studiach
II stopnia.
13.2-4-QE/II/1
Quantum Electrodynamics
Course title
Quantum Electrodynamics
Course type
obligatory
Course level
advanced level; 1st semester of Master studies
ETCS points
Name of the lecturer
prof. dr hab. Ludwik Turko
Objective of the course
The aim of the lecture is to present quantum electrodynamics as a tool
to solve physical problems related to the electromagnetic interaction
which have no satisfactory solution within classical physics or quantum
mechanics.
Prerequisities
Knowledge in basic and advanced quantum mechanics, classical
electrodynamics, classical field theory.
Contents of the course
1. Radiation and emission problems
2. Quantum fields as a generalization of quantum mechanics.
3. Klein-Gordon, Dirac and electromagnetic field quantization.
4. Field theoretic description of electromagnetic interaction
5. Radiative corrections.
6. Renormalization schemes.
7. Bound state problems
8. Quantum electrodynamics as an introduction to nonabelian gauge
theories.
Recommended reading
1. C. Itzykson, J.-B. Zuber, Quantum Field Theory
2. S.Weinberg, Theory of Fields, vol. 1 Foundations
3. J. D. Bjorken, S. D. Drell, Relativistic Quantum Mechanics,
Relativistic Quantum Fields
Teaching method
lecture - 2 hrs per week (30 hours in total)
classes - 2 hrs per week (30 hours in total)
Assessment method
Language of instruction
classes grade - solving problems during semester, written test at the end
of semester
exam grade - oral or written exam at the end of semester
English
13.2-4-CFT/II/1
Classical Field Theory
Course title
Course type
Course level
Classical Field Theory
obligatory
advanced level; 1st semester of Masters studies
108
ETCS points
Name of the lecturer
Objective of the course
Prerequisities
Contents of the course
Recommended reading
Teaching method
Assessment method
Language of instruction
13.2-4-SM/II/1
Statistical Mechanics II
Course title
Course type
Course level
ETCS points
Name of the lecturer
Objective of the course
Prerequisities
Contents of the course
prof. dr hab. Jerzy Kowalski Glikman
The aim of this course is to introduce the basic concepts of classical
field theory, gauge theory and supersymetry.
Basic knowledge in classical mechanics, special relativity and classical
electrodynamics.
1. Introduction. Action and equations of motion. Symmetries.
2. Canonical formalism of mechanics. Noether theorem.
3. Variational principle in field theory. Noether theorem. Energymomentum tensor.
4. Lagrangians of free fields; examples.
5. Relativistic particle. Fermions. Supersymmetry in one dimension.
6. Gauge fields I: Electrodynamics
7. Gauge fields II: Yang-Mills fields. Gribov ambiguity.
8. Gauge fields III: Spontaneous symmetry breaking and standard
model of elementary particles.
9. Monopoles in abelian and non-abelian gauge theory.
10. Instantons.
11. Canonical analysis in field theory. Constraints. Canonical analysis
of Chern-Simon theory.
12. BRST symmetry in gauge theories.
13. Supersymmetric field theories.
P. Ramond, Field Theory A Modern Primer
R. Rajaraman, Solitons and Instantons
1 semester
lecture - 2 hrs per week (30hours In total)
classes - 2 hrs per week (30hours In total)
classes grade - solving problems during semester, written test at the
end of semester
exam grade - oral or written exam at the end of semester
English
Statistical Mechanics II
obligatory for theoretical physics students
advanced level; 1st semester of Master studies
dr hab. Janusz Jędrzejewski, prof.U.Wr.
The aim of this course is to explain basic concepts and methods of
modern statistical physics to students specialized in field theory.
Statistics or constraints as a source of effective interactions. Mean-field
description of condensed matter systems. Stability of matter. The
ferromagnetic and antiferromagnetic states as instances of a coexistence
of phases and first-order phase transitions. One-dimensional Ising
model. Two-dimensional Ising model. The Ising model; rigorous
results. A brief look at rigorous theories of low-temperature properties
of classical lattice systems. The Hubbard and Falicov-Kimball models
of strongly correlated electrons
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Recommended reading
Teaching method
Assessment method
Language of instruction
13.2-4-QFT1/II/2
Quantum Field Theory 1
Course title
Course type
Course level
ETCS points
Name of the lecturer
Objective of the course
Prerequisities
Contents of the course
Recommended reading
Teaching method
Assessment method
Language of instruction
13.2-4-QFT2/II/3
Quantum Field Theory 2
Course title
Course type
Course level
ETCS points
Name of the lecturer
Objective of the course
1. Colin J. Thompson, Mathematical Statistical Mechanics
2. R.J. Baxter, Exactly Solved Models in Statistical Mechanics
3. F.H.L. Essler, H. Frahm, F. Gohmann, A. Klumper, V.E. Krepin,
The One-Dimensional Hubbard Model
4. G. Giuliani, G. Vignale, Quantum Theory of the Electron Liquid
lecture - 2 hrs per week (30 hours in total)
classes - 2 hrs per week (30 hours in total)
classes grade - solving problems during semester, written test at the end
of semester
exam grade - oral or written exam at the end of semester
English
Quantum Field Theory 1
obligatory
advanced level; 2nd semester of Masters studies
dr hab. David Blaschke, prof.U.Wr.
The aim of the lecture is to provide an introduction to advanced
methods of quantum field theory. The first part of this lecture is
devoted to path integral techniques and renormalization.
Knowledge in basic and advanced quantum mechanics, quantum
electrodynamics and classical field theory.
1. Invitation: Pair Production in e+e- Annihilation
2. The Klein-Gordon Field
3. The Dirac Field
4. Interacting Fields and Feynman Diagrams
5. Elementary Processes: e+e- and pion-pion scattering
6. Functional Methods: Path Integral Quantization
7. Systematics of Renormalization
8. The Renormalization Group
9. Quantum Chromodynamics
1. M.E. Peskin, D.V. Schroeder: Quantum Field Theory
2. Zee: Quantum Field Theory in a Nutshell
3. B. DeWit, J. Smith: Field Theory in Particle Physics
lecture - 2 hrs per week (30 hours in total)
classes - 2 hrs per week (30 hours in total)
classes grade - solving problems during semester, written test at the end
of semester
exam grade - oral or written exam at the end of semester
English
Quantum Field Theory 2
obligatory
advanced level; 3rd semester of Masters studies
dr hab. David Blaschke, prof.U.Wr.
The aim of the lecture is to provide an introduction to advanced methods
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Prerequisities
Contents of the course
Recommended reading
Teaching method
Assessment method
Language of instruction
of quantum field theory. The second part of this lecture is devoted to
non-abelian gauge theories and collective phenomena.
Knowledge in basic and advanced quantum mechanics, quantum
electrodynamics and classical field theory.
1. Non-Abelian Gauge Invariance
2. Quantization of Non-Abelian Gauge Theories
3. Renormalization and Gauge Invariance
4. Gauge Theories and Spontaneous Symmetry Breaking
5. Field Theory and Collective Phenomena
6. Field Theory and Condensed Matter
7. Grand Unification? Open Questions
1. M.E. Peskin, D.V. Schroeder: Quantum Field Theory
2. Zee: Quantum Field Theory in a Nutshell
3. B. DeWit, J. Smith: Field Theory in Particle Physics
lecture - 2 hrs per week (30 hours in total)
classes - 2 hrs per week (30 hours in total)
classes grade - solving problems during semester, written test at the end
of semester
exam grade - oral or written exam at the end of semester
English
11.1-4-MMTP/II/1
Mathematical Methods in Theoretical Physics
Course title
Mathematical Methods in Theoretical Physics
Course type
obligatory
Course level
advanced level; 1st semester of Masters studies
ETCS points
Name of the lecturer
prof. dr hab. Robert Olkiewicz
Objective of the course
The aim of this course is to give the basic knowledge of structures and
results of differential geometry which are important for modern
applications in gauge theory and general relativity.
Prerequisities
Basic knowledge in calculus and linear algebra.
Contents of the course
1. Preliminaries
1.1. Elements of linear and multi-linear algebra
1.2. Review of differential calculus of functions
1.3. Elements of topology
2. Differential manifolds and vector bundles
2.1. Smooth differential manifolds
2.2. Tangent space and tangent bundle
2.3. Vector fields, tensor fields and p-forms
2.4. Riemannian manifolds
3. Linear connections
3.1. Local one-parameter transformation groups
3.2. Linear connections, Christoffel's symbols
3.3. The tensors of curvature and torsion
3.4. Covariant derivatives, the Levi-Civita connection
3.5. Geodesic lines
Recommended reading
1. L. Conlon, Differentiable Manifolds
2. B.A. Dubrovin, A.T. Fomenko, S.P. Novikov, Modern Geometry –
Methods and Applications: Part I
3. J.M. Lee, Introduction to Smooth Manifolds
4. M. Spivak, A Comprehensive Introduction to Differential Geometry
Teaching method
lecture - 2 hrs per week (30 hours in total)
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Assessment method
Language of instruction
classes - 2 hrs per week (30 hours in total)
classes grade - solving problems during semester, written test at the end
of semester
exam grade - oral or written exam at the end of semester
English
13.2-4-EPT/II/2
Elementary Particle Theory
Course title
Elementary Particle Theory
Course type
obligatory for theoretical physics students
Course level
advanced level; 2nd semester of Master studies
ETCS points
Name of the lecturer
dr hab. Ludwik Turko, prof.U.Wr.
Objective of the course
The aim of the lecture is to provide basic knowledge of elementary
interactions, excluding gravitational forces.
Prerequisities
Knowledge in basic and advanced quantum mechanics, classical
electrodynamics, classical field theory.
Contents of the course
1. Scattering processes, production and decays of elementary
particles.
2. Internal and space-time symmetries.
3. Properties of basic interactions: weak, electromagnetic, strong.
4. Basic characteristic of elementary particles.
5. Elements of field theory, gauge fields, Feynman diagrams
6. The role of symmetries and conservation laws: hadrons and their
SU(3) and SU(4) spectroscopy, selection rules, phenomenology of
weak interaction, SU(2)XU(1) electroweak interaction, SU(3)
chromodynamics, SU(5) unification scheme.
7. Collective phenomena in dense hadronic matter: quark-gluon
plasma, neutron and quark stars.
Recommended reading
1. D.H.Perkins. Introduction to high energy physics, Cambridge 2000
2. K.Gottfried, V.F.Weisskopf, Concepts of Particle Physics, Oxford
1984
3. D.Griffiths, Introduction to Elementary Particles, Wiley 1987
4. B.F.Schutz, A First Course in General Relativity, ch. 1,2,3,
Cambridge 1985
5. E.Byckling, K.Kajantie, Particle Kinematics, Wiley 1973
Teaching method
lecture - 2 hrs per week (30 hours in total)
classes - 2 hrs per week (30 hours in total)
Assessment method
classes grade - solving problems during semester, written test at the end
of semester
exam grade - oral or written exam at the end of semester
Language of instruction
English
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13.2-4-GR/II/2
General Relativity
Course title
Course type
Course level
ETCS points
Name of the lecturer
Objective of the course
Prerequisities
Contents of the course
Recommended reading
Teaching method
Assessment method
Language of instruction
General Relativity
obligatory for theoretical physics students
advanced level; 2nd semester of Masters studies
prof. dr hab. Jerzy Kowalski Glikman
The aim of this course is to provide a comprehensive introduction to
general relativity.
Basic knowledge in classical electrodynamics, classical field theory and
differential geometry.
1. Tetrad as gravitational field.
2. Length, area, volume. Covariant differential. Connection. Torsion.
Curvature.
3. Einstein action and Einstein equations.
4. Metric formulation of GR.
5. The meaning of general relativity: Diffeomorphism invariance;
Observables in general relativity.
6. Conceptual path to the theory: Newton’s bucket; Mach principle;
The hole argument.
7. GPS satellites and the meaning of coordinates in GR.
8. Geodesics in Schwarzschild geometry: Perihelion precession;
bending of light; delay of radar signals.
9. Schwarzschild geometry: Solution of Einstein field equations;
global structure; Penrose diagrams.
10. Weak gravitational field and gravitational waves.
11. Taub-NUT solution.
12. Introduction to cosmology: FRW spacetime. History of the
Universe.
1. James B. Hartle, Gravity: An Introduction to Einstein's General
Relativity
2. Sean Carroll, Spacetime and Geometry: An Introduction to General
Relativity
3. Robert M. Wald, General Relativity
lecture - 2 hrs per week (30 hours in total)
classes - 2 hrs per week (30 hours in total)
classes grade - solving problems during semester, written test at the end
of semester
exam grade - oral or written exam at the end of semester
English
WYKŁADY MONOGRAFICZNE
11.1-4-AMTP/II/1
Algebraic Methods in Theoretical Physics
Course title
Algebraic Methods in Theoretical Physics
Course type
Optional
Course level
Second degree studies (semester 1)
ETCS points
Name of the lecturer
Marek Mozrzymas, dr hab.
Objective of the course
An introduction to basic algebraic structures appearing in theoretical
physics and to theory of linear operators in finite dimensional linear
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spaces. A comprehensive introduction to linear representation theory of
finite groups and Lie algebras.
Prerequisities
Contents of the course
Recommended reading
Teaching method
Assessment method
Language of instruction
13.2-4-MC/II/3
Modern Cosmology
Course title
Course type
Course level
ETCS points
Name of the lecturer
Objective of the course
Prerequisities
Contents of the course
Recommended reading
Teaching method
Assessment method
Language of instruction
I. Algebraic structures.
Groups, rings, fields, algebras, modules and homomorphisms.
II. Linear operators.
1. Algebra of linear operators. Invariant subspaces. Minimal
polynomials. Jordan decomposition of linear operator.
2. Linear operators in spaces with scalar product. Polar
decomposition of linear operator.
3. Complexification of real linear spaces.
III. Finite groups.
1. Structure of finite groups: simple, solvable and abelian groups.
2. Elements of representation and character theory.
3. Representations of symmetric group and Young diagrams.
IV. Lie algebras.
1. Simple and semisimple Lie algebras.
2. Weights and roots. Weyl group. Cartan matrix.
3. Representations of semisimple Lie algebras. Killing fom. Casimir
operators. Weight diagrams.
V. Matrix (linear) groups.
1. Functions Exp and Log of a matrix. B-H-C formula.
2. One-parameter subgroups.
3. Lie algebra of a linear group.
1. A. I. Kostrykin: „Wstęp do algebry”, PWN
2. A. O. Barut, R, Rączka: „Theory of Group Representation and
Applications”, PWN
3. L. Górniewicz, R. S. Ingarden: „Algebra z Geometrią dla
Fizyków”, UMK
Lecture, 2 hours per week during 15 weeks.
A grade based on solutions of problems given during the lecture
English
Modern Cosmology
Optional
Advanced level; Second degree studies (semester 3)
Jerzy Kowalski-Glikman, prof. dr hab.
To get students acquainted with modern cosmology on qualitative level.
Hubble law. Friedmann model. Evolution of the universe. Thermal
history of the universe. Nucleosynthesis. Cosmological inflation.
Formation of structures in the universe (within Newtonian model).
Cosmic Microwave Background spectrum: theory and observations.
1. V. Mukhanov Physical Foundations of Modern Cosmology
2. A. Liddle An Introduction to Modern Cosmology
Lectures - 2 lectures weekly for 15 weeks
Students write an essay, discussing given problem in depth, and they
solve some number of exercises.
English
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WYKŁADY SPECJALISTYCZNE
13.2-4-ISTDD/II/
Introduction to String Theory and D-brane Dynamics
Course title
Introduction to String Theory and D-brane Dynamics
Course type
Optional
Course level
Advanced level; Second degree studies of theoretical physics
ETCS points
Name of the lecturer
Zbigniew Jaskólski dr hab., prof UWr.
Objective of the course
The lectures are intent to provide students with the rudiments of
perturbative string theory and an elementary introduction to the D-brane
dynamics.
Prerequisities
Contents of the course
Classical String Theory. Quantization of Bosonic String. Superstrings.
Ramond-Ramond charges and T-Duality. D-branes and Gauge Theory.
D-brane Dynamics
Recommended reading
1. R.J.Szabo An Introduction to String Theory and D-brane
Dynamics
2. C.V.Johnson D-Branes
3. K.Becker, M.Becker, J.E.Schwarz String Theory and M-Theory
Teaching method
Lectures - 2 lectures weekly for 15 weeks
Assessment method
Students solve a number of problems in writing. Oral exam at the end of
semester.
Language of instruction
English
13.2-4-MOC/II
Mechanika ośrodków ciągłych - przedmiot opisany przy specjalności Fizyka komputerowa.
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