1. SylabUZ
2. Faculty of Physics and Astronomy
3. winter term 2019/2020
4. Physics - Second-cycle studies leading to MS degree
5. Field theory

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Field theory - course description

Aim of the course

The aim of the course is to familiarize students with the formalism of special and general theories of relativity, the similarities and differences between them, and their applications to the description of certain physical and astronomical phenomena.

Prerequisites

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Mathematical Analysis I and II, mathematical physics, algebraic and geometric methods in physics

Scope

- Spacetimes of Aristotle, Galileo, and Newton, the concept of the inertial system, absolute and relative character of the time and spatial distances between events, the geometry of the spacetime. Principles of relativity: Galileo's principle and Einstein's principle. Einstein's postulates.
- The Lorentz transformation, addition of velocities, constant velocity of light in various inertial frames, the time dilation and relativity of simultaneity, the contraction of distances.
- Space-time of the special theory of relativity: the event , the world line of a particle, thw cone of light , space-time interval , the classification of intervals, four vectors.
- Spacetime of general relativity , the relationship between spacetimes of general and special relativity , the local inertial frames.
- The principle of equivalence, relativity, minimal gravitational coupling and correspondence.
- Geodesic deviation and Einstein's equations in empty space. Newtonian limit of geodesic equations.
- Tensors of energy and momentum.
- Einstein's equations.
- The structure of Einstein's equations and their general properties.
- The Schwarzschild's solution.

Teaching methods

Conventional lecture with applications of trained formalism to some physical and astronomical systems and phenomena.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

Lecture:

The course credit is obtained by passing a final written exam containing tasks of varying degrees of difficulty.

Class:

A student is required to obtain at least the lowest passing grade from the test organized during class.

To be admitted to the test from the content of lecture a student must receive a credit for the class.

Final grade: weighted average of grades from the class (40%) and the written texam from the content of lecture (60%).

Recommended reading

[1] W. A. Ugarow, Special theory of relativity, Mir Publisher, Moscow, 1979, Polish translation: Szczególna teoria względności, PWN, Warszawa 1985.

[2] J. Foster, J. D. Nightingale, A short course in general relativity, third edition, Springer, 2003, Polish translation: Ogólna teoria względności, PWN, Warszawa 1985.

[3] J. B. Hartle, Gravity. An introduction to Einstein's general relativity, Addison Wesley, 2003, Polish translation:  Grawitacja, Wprowadzenie do ogólnej teorii względności Einsteina, Wydawnictwo Uniwerystetu Warszawskiego, 2010.

[4] L. D. Landau, J. M Lifszyc, The classical theory of fields, fourth edition, Butterworth Heinemann, Polish translation: Teoria pola, Wydawnictwo Naukowe PWN, Warszawa 2009.

[5] R. D'Inverno, Introducing Einstein's relativity, Claredon Press, Oxford 1998.

[6] M. P. Hobson, G. Efstathiou, A. N. Lasenby, General relativity: an introduction for physicists, Cambridge University Press, Cambridge 2006.

Further reading

[1] B. F. Schutz, A first course in general relativity, second edition, Cambridge University Press, 2009, Polish translation: Wstęp do ogólnej teorii względności, Wydawnictwo Naukowe PWN, Warszawa 2002.

Notes

Modified by dr hab. Piotr Lubiński, prof. UZ (last modification: 05-03-2020 18:01)