Code: 02TEF2 Theoretical Physics 2
Lecturer: Ing. Petr Novotný Ph.D. Weekly load: 2+2 Completion: A, EX
Department: 14102 Credits: 4 Semester: S
Description:
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.
Contents:
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
Seminar contents:
Solving problems to illustrate the theory from the lecture
Recommended literature:
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.
Keywords:
tensor, transformation, symmetry, rigid body, continuum ,the Minkowski spacetime, the interval, the Lorentz transformations, equations of motion for a relativistic particle, Maxwell's equations in a medium, potentials of the electromagnetic field, Maxwell's equations in the Minkowski spacetime, retarded potentials, electric dipole radiation, stress tensor, strain tensor, Euler's equations

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