Pavel Krtouš

Introduction to the modern description of the electromagnetic field and advanced methods used in solving field equations.

Maxwell's equations. Methods of solution. Static, stationary, and quasistationary approximation. Conservation laws. Relativistic formulation. Dynamical theory and electromagnetic radiation.

The course is intended for second-year undergraduate physics students.

The course is alternately led by P. Krtouš and T. Ledvinka.

Taught in Czech only.

The introduction to Special Theory of Relativity – the theory of space and time that forms the foundation of all modern fundamental descriptions of the world.

Experimental basis and foundational principles of the Special theory of relativity. Relativistic kinematics: causal structure, inertial frames, Lorentz transformation, Minkowski spacetime. Tensor formulation of physical laws. Relativistic effects. Relativistic dynamics: collisions, mechanics, electrodynamics. Variational principles.

The course is intended for second-year undergraduate physics students.

Taught in Czech only.

The course was taught by P. Krtouš in 2018 and 2021.

taught together with R. Švarcem

The proseminar is a supplementary course focused on methods of mathematical physics and their application in introductory physics courses.

Review of derivatives and Taylor expansion. Tangent vector and gradient. Spatial coordinates and vector components. Differential equations. Matrix calculus. Moving reference frames. Integration along curves, surfaces, and in space. Gradient, curl, divergence operators, and integral theorems.

The proseminar is intended for first-year physics students.

Taught in Czech only.

taught together with O. Svítek

This is a supplementary course focused on methods of mathematical physics and their application in modern theoretical physics. Emphasis is placed on the mathematical apparatus used in the parallel lectures on Classical Electrodynamics and Introduction to Quantum Mechanics.

Vectors and tensors. Curvilinear coordinates and vector analysis. Introduction to distribution theory, Fourier transform, distributions in 3D, Green's functions. Classical field theory, Lagrangian and Hamiltonian formalism, gauge symmetry. Multipole expansion in tensor form. Feynman formulation of quantum mechanics, probability rules, path integral.

The proseminar is intended for second-year physics students.

Taught in Czech only.

course author: P. Krtouš, taught together with R. Švarc and I. Kolář

Introduction to the differential geometry with an emphasis on applications in physics.

Tensor calculus. Differentiable manifolds and tangent spaces. Basics of fiber bundles. Mappings of manifolds, diffeomorphisms, Lie derivative. Exterior calculus. Riemannian and pseudo-Riemannian geometry. Covariant derivative, parallel transport, geodesics. Torsion and curvature, space of connections. Metric derivatives, Levi-Civita connection. Relationship between the Lie, exterior, and covariant derivatives. Submanifolds. Integration on manifolds, densities, integral theorems.

The course is intended primarily for students of theoretical physics towards the end of their bachelor's or the beginning of their master's studies.

The course is followed by the subjects Geometric Methods – Advanced Topics A and B (NTMF060, NTMF160).

Taught mostly in Czech, in some years in English.

course author: P. Krtouš, taught together with R. Švarc and I. Kolář

Selected topics in advanced geometrical methods in physics.

Hodge theory. Topological methods – cohomology a homology groups, homotopy, Poincare lemma. Curvature splitting on submanifolds. Fibre bundles, geometry of gauge fields, characteristic classes. Fiber bundles with a soldering form, the tetrad formalism. Complex spaces, charged fields. Geometry of Lie groups and algebras. Lie algebras and their representations, Casimir operators. The orthogonal group. Clifford algebras, spinors. Covariant derivative on spinors, the Dirac operator.

The topics are offered in two alternating and independent lecture courses, NTMF060 and NTMF160.

Basic knowledge of differential geometry at the level of the course NTMF059 is assumed.

The lectures are intended primarily for students of theoretical physics in their master's and doctoral studies.

Taught mostly in Czech, in some years in English.

Foundations and interpretations of quantum mechanics, focusing in particular on the nature of quantum measurement. The aim is to introduce various formulations of quantum mechanics, their mutual relations, advantages, and problems.

• Standard quantum mechanics
  • appearance of the quantum world on the scene
  • nature of the quantum description
  • quantum states and the measurement process
  • specification of a quantum system
  • statistical description
  • time evolution
  • composite systems
  • quantum measurement and the nature of state reduction
  • collapse in relativistic theory
  • interpretations and their problems
• Hidden variable theories
  • motivation
  • Bell's inequalities
  • quantum strategies
• Measurement theory
  • position measurement via instantaneous interaction
  • Stern-Gerlach experiment
  • decoherence and effective reduction
• Many-worlds interpretation of quantum mechanics
  • quantum mechanics without collapse
  • quantitative predictions
  • one and two observers
• Feynman formulation of quantum mechanics
  • histories and systems of histories
  • quantum indistinguishability
  • structure of histories
  • rules for amplitudes and probabilities
• Generalized quantum mechanics
  • Wigner formula
  • interference and decoherence
  • consistency of histories
  • decoherence functional and decohering histories

The course is primarily intended for 3rd and 4th-year students as a supplementary lecture course to quantum mechanics. Ph.D. students and other interested parties are also welcome.

Taught in Czech only.

Quantization of physical fields in curved spacetime, i.e., in the presence of a classical gravitational field.

Hamiltonian formalism in field theory, 3+1 splitting. Quantization on a curved background, Fock basis, coherent states, vacuum state, normal ordering, Bogoliubov transformation, S-matrix, generating functional. Static spacetimes, diagonalization of the Hamiltonian, thermal states, Green functions, their analytical properties and singular structure, Wick rotation. Moving mirrors, cosmological particle creation, Unruh effect, particle detectors. Hawking effect, choice of modes and vacuum state. Theormodynamics of black holes. Quantization in de Sitter spoacetime.

Intended for master's and doctoral students.

Knowledge of general relativity and quantum mechanics at the level of introductory lecture courses is assumed. Knowledge of quantum field theory is a great advantage but not a strict prerequisite.

Taught mostly in Czech, in some years in English.

the course is jointly taught by P. Cejnar, P. Krtouš, and J. Podolský

An open series of lectures dedicated to key concepts that represent milestones in the development of physics and form its contemporary foundation.

Each of the lecturers runs two independent half-semester cycles, meaning the entire course has a three-year periodicity.

P. Krtouš leads the cycles The Story of Inertia and Gravity and The Quantum World. P. Cejnar leads the cycles Discovering the Quantum World and Particles, Fields, Interactions, and Complexity. J. Podolský gives lectures on the cycles From the Origins of Astronomy to the Theory of Gravity and Into the Depths of the Universe.

The lectures are intended primarily for second-year students of the Faculty of Mathematics and Physics, Charles University, but students from all faculties of Charles University and other interested parties are also welcome.

Taught in Czech only.

a series of lectures by various speakers

A seminar dedicated to philosophically motivated topics from the present and history of physics, with an emphasis on its natural science and cultural context.

Within this seminar, P. Krtouš has delivered over 40 lectures over the past 30 years.

Taught in Czech only.