F5510 The canonical formalism of classical mechanics and field theory

Faculty of Science
Autumn 2008
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Novotný, CSc. (lecturer)
Mgr. Pavel Klepáč, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Plasma Physics and Technology – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Jan Novotný, CSc.
Timetable
Thu 7:00–7:50 Fs2 6/4003, Fri 11:00–12:50 F4,03017
Prerequisites
Knowledge of fundaments of classical mechanics, electrodynamics and special relativity.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The Lagrange and Hamilton formalism in classical mechanics and relativistic field theory,variational principles, principles and symmetry and conservation laws - theorems of E. Noether,the canonical and symmetrical tensors of energy-momentum, connections between classical and quantum mechanics,mathematical fundaments of general theory of relativity. The main aim of this lecture is: to understadn formal basis of modern theoretical physics; to acquire connections between symmetries, conservation laws and equations of motion to obtain ability to read contemporary physical literature
Syllabus
  • Lagrangean formalism in the classical mechanics
  • First theorem of E. Noether in the classical mechanics
  • Lagrangean formalism in the field theory
  • Connections between symmetries, conservation laws and field equations
  • Second theorem of E. Noether
  • Energy-momentum tensors
  • Hamiltonian formalism, canonical transformations
  • Hamilton - Jacobi equation
  • Connection between classical mechanics, quantum mechanics and statistical physics
  • Mathematical foundations of general theory of relativity
Literature
  • KRUPKA, Demeter. Lectures on differential invariants. Edited by Josef Janyška. Vyd. 1. Brno: Univerzita J.E. Purkyně, 1990, 193 s. ISBN 8021001658. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. The classical theory of fields. Translated by Morton Hamermesh. 4th rev. Engl. ed. Oxford: Elsevier Butterworth-Heinemann, 1975, xiii, 428. ISBN 0-7506-2768-9. info
  • LANDAU, Lev Davidovič and Jevgenij Michajlovič LIFŠIC. Mechanics. Translated by J. B. Sykes - J. S. Bell. 2nd ed. Oxford: Pergamon Press, 1969, vii, 165. info
Assessment methods
credit for appropriate participation in the exercizes oral exam
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2008, recent)
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