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Introductory Seminar on Theoretical Physics - NOFY070

Title:	Proseminář z teoretické fyziky
Guaranteed by:	Laboratory of General Physics Education (32-KVOF)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	summer
E-Credits:	2
Hours per week, examination:	summer s.:0/2, C [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://utf.mff.cuni.cz/vyuka/NOFY070

Guarantor:	prof. RNDr. Pavel Krtouš, Ph.D. doc. RNDr. Otakar Svítek, Ph.D.
Classification:	Physics > Theoretical and Math. Physics

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: doc. RNDr. Karel Houfek, Ph.D. (14.05.2021)

Vector and tensor calculus, curvilinear coordinates. Introduction to distributions, Fourier transformation, Green functions. Introduction to classical field theory. Multipole expansion in a tensor form. Feynman formulation of quantum mechanics.

Course completion requirements - Czech

Last update: prof. RNDr. Pavel Krtouš, Ph.D. (29.01.2021)

Zápočet bude udělen za dostatečnou účast na hodinách a správné vypracování domácích úloh.

Povaha kontroly splnění podmínek pro udělení zápočtu vylučuje opakování této kontroly, tedy zápočet se opakovat nedá.

Literature - Czech

Last update: prof. RNDr. Pavel Krtouš, Ph.D. (29.01.2021)

K. Kuchař: Základy obecné teorie relativity, Academia, Praha 1968.

L. Schwartz: Matematické metody ve fyzice, SNTL, Praha 1972

J. W. Leech: Klasická mechanika, SNTL, Praha 1970.

R. P. Feynman, R. B. Leighton, M. L. Sands, Feynmanovy přednášky z fyziky 3, Fragment, Havlíčkův Brod 2002.

R. P. Feynman: Neobyčejná teorie světla a látky, Aurora, Praha 2001.

Syllabus -

Last update: prof. RNDr. Pavel Krtouš, Ph.D. (29.01.2021)

Vectors and tensors.: Affine space, vectors and linear forms, tensors, coordinate transformations, diagrammatic notation, scalar product and metric.
Curvilinear coordinates and vector analysis.: Tensor fields, gradient and nabla-operator, curvilinear coordinates, triads. Integrating vectors and tensors.
Introduction to distributions.: Basic definitions and properties, δ-distribution, derivatives of non-smooth functions, regularization of 1/x. Fourier transformation of distribution, examples. Distribution on manifolds, characteristic function, surface and linear δ-distributions and their derivatives. Aplications: point, linear and surface sources, dipoles, boundary conditions for electrostatic a magnetostatic, electric field near conductors.
Green functions: Green functions in one variable. Green function for Laplace operator, Laplace equation on a domain with a boundary, heat equation, perturbative solution of Schrödinger equation with potential.
Classical field theory: Lagrange and Hamilton formalism for fields, scalar and electromagnetic field, gauge symmetry.
Supplements for classical electrodynamics: Multipole expansion in terms of tensors. Description of continuum is spacetime, stress-energy tensor, electric current density, conservation laws.
From sum over trajectories to solution of differential equations.: Feynman's formulation of quantum mechanics: quantum histories, quantum indistinguishability, amplitude rules, measurement model. Path integral, amplitude of free particle evolution, perturbative solution of Schrödinger equation.