Theoretical Physics 2

Relations:

In order to register for the course 02TEF2, the student must have successfully completed in previous semesters the required number of courses in the group PREREKKF1.

Course guarantor:

Petr Novotný

Lecturer:

Petr Novotný

Tutor:

Filip Moučka, Petr Novotný, Filip Petrásek, Josef Schmidt

Supervisor:

Department of Physics

Synopsis:

Tensors and transformations in physics. Mechanics of point mass, rigid body and continuum. The special theory of relativity: relativistic mechanics and classical field theory in the Minkowski space-time. Classical electrodynamics: Maxwell's equations in the Minkowski space-time, electromagnetic waves in dielectric media, electromagnetic radiation in the dipole approximation.

Requirements:

02TEF1 - Theoretical Physics 1

02ELMA - Electricity and Magnetism

Syllabus of lectures:

1. Physical quantities, units, Tensor calculus, operations with tensors, transformation of tensor components

2. Tensor product, invariant tensors, second order tensors, metric tensor, covariant and contravariant components, orientation, pseudo-tensors

3. Affine space, rectilinear coordinates, curvilinear coordinates, symmetry of affine space, affine group, Tensor fields: their transformations and symmetries, Newton's absolute time and space

4. Newtonian mechanics, Euclidean affine space, 1st Newton's law, inertial reference frame, Galilei's principle of relativity, Galilei's group of transformations, 2nd Newton's law in non-inertial reference frame, angular velocity pseudovector

5. Rigid body mechanics, moment of inertia tensor, rigid body motion, Euler's equations, Euler's angles, top and its motion

6. Continuum mechanics, surface and body forces, stress tensor, equation of motion for continuum

7. Euler's equations (fluid dynamic), elastic continuum, strain tensor, Hooke's law, Lamé's equation

8. Special relativity, Lorentz transformations, interval, Minkowski spacetime, Lorentz group, Poincaré group

9. Relativistic generalization of Newton's equation of motion, four-momentum, relativistic energy, particle collisions and decays, Lagrange and Hamiltonian functions for a charged relativistic particle

10. Maxwell's equations, continuity equations, scalar and vector potential, calibration transformation, Lorenz calibration condition

11. Electrodynamics equations in Minkowski spacetime, electromagnetic field tensor, Lorentz four-force, relativistic invariants of elmag. field

12. Lagrangian formalism in field theory, Hamilton's principle for fields, equation of motion for fields, Action for a system of charged particles and elmag. field, Conservation laws in field theory, conserved 4-current

13. Noether's theorem for fields, canonical energy-momentum tensor, symmetrical energy-momentum tensor

Syllabus of tutorials:

Solving problems to illustrate the theory from the lecture

Study Objective:

Knowledge:

Learn the basics of tensor calculus. Learn about the space on which Newtonian mechanics (Euclidean affine space) and special relativity (Minkowski spacetime) take place. Learn about groups of transformations and their role in physics: Galilei group (Galilei's principle of relativity), Lorentz group (Einstein's principle of relativity).

Apply knowledge of the tensor calculus to describe rigid body motion (moment of inertia tensor), the continuum (stress tensor and strain tensor), the electromagnetic field (electromagnetic field tensor, energy and momentum tensor).

Learn the basics of the Lagrangian formalism in classical field theory and apply them to the description of the electromagnetic field in Minkowski spacetime. This is the second part of the classical theoretical physics course at FNSPE.

Skills:

Application of methods of theoretical physics to solve concrete examples.

Study materials:

Key references:

[1] H. Goldstein, C. P. Poole, J. Safko: Classical Mechanics, Pearson Education; 3rd edition, 2011

[2] E. C. G. Sudarshan, N. Mukunda: Classical Dynamics: A Modern Perspective, World Scientific; Reprint edition, 2015

[3] D. J. Griffiths: Introduction to Electrodynamics, Cambridge University Press; 4 edition, 2017.

Recommended references:

[4] G. Joos, I. Freeman: Theoretical Physics, Courier Corp. 2013.

[5] J. D. Jackson: Classical Electrodynamics, Wiley, New York, 1962. (available in the library of FJFI ČVUT)

[6] L. D. Landau, E. M. Lifšic, Course of Theoretical physics, Elsevier, 2013.

Note:

Further information:

https://physics.fjfi.cvut.cz/index.php/cs/studium/predmety-na-kf/02tef12-teoreticka-fyzika-1-a-2

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální inženýrství - Počítačová fyzika (PS)
• Aplikovaná algebra a analýza (compulsory course in the program)
• Fyzikální inženýrství - Fyzikální inženýrství materiálů (elective course)
• Fyzikální inženýrství - Fyzika plazmatu a termojaderné fúze (elective course)
• Fyzikální inženýrství - Inženýrství pevných látek (PS)
• Jaderná a částicová fyzika (compulsory course in the program)
• Fyzikální inženýrství - Laserová technika a fotonika (PS)
• Matematické inženýrství - Matematická fyzika (PS)
• Matematické inženýrství - Matematická informatika (elective course)
• Kvantové technologie (compulsory course in the program)
• Physical Engineering - Computational physics (PS)
• Quantum Technologies (compulsory course in the program)
• Nuclear and Particle Physics (compulsory course in the program)
• Physical Engineering - Physical Engineering od Materials (elective course)
• Mathematical Engineering - Mathematical Physics (PS)
• Physical Engineering - Plasma Physics and Thermonuclear Fusion (elective course)