SubjectsSubjects(version: 916)
Course, academic year 2022/2023
   Login via CAS
Introduction to the theory of Loop Quantum Gravity - NTMF080
Title: Úvod do teorie smyčkové kvantové gravitace
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Additional information:
Guarantor: RNDr. Otakar Svítek, Ph.D.
prof. RNDr. Pavel Krtouš, Ph.D.
Classification: Physics > Theoretical and Math. Physics
Annotation -
Last update: doc. RNDr. Karel Houfek, Ph.D. (13.05.2022)
Loop Quantum Gravity is one of the candidates for the theory of quantum gravity, which is background independent and does not require renormalization. The main aim of these lectures is to understand its kinematical formulation. Starting from the Einstein-Palatini-Holst Lagrangian we perform its classical Hamiltonian analysis. Ashtekar variables and Loop representation are introduced. Dirac’s approach to constrained systems and Algebraic Quantization are employed. Volume and Area operators possessing discrete spectra are constructed. Intended for advanced graduate and postgraduate students.
Course completion requirements - Czech
Last update: doc. RNDr. Karel Houfek, Ph.D. (11.06.2019)

Ústní zkouška

Literature -
Last update: T_UTF (27.04.2016)

T.Thiemann: Modern Canonical Quantum General Relativity (Cambridge, 2007)

A. Ashtekar, J. Lewandowski, Background Independent Quantum Gravity: a Status Report, Class.Quant.Grav.21:R53,2004 (

A.Ashtekar, J.Lewandowski, D.Marolf, J.Mourao, T.Thiemann: Quantization of diffeomorphism invariant theories of connections

with local degrees of freedom,J.Math.Phys.36:6456-6493,1995 (

A.Ashtekar, J.Lewandowski : Representation Theory of Analytic Holonomy C* Algebras,

in Knots and Quantum Gravity (ed. J.Baez, Oxford U.Press) (

Requirements to the exam - Czech
Last update: doc. RNDr. Karel Houfek, Ph.D. (11.06.2019)

Zkouška je ústní, požadavky odpovídají sylabu, v detailech pak tomu, co bylo během semestru odpřednášeno.

Syllabus -
Last update: T_UTF (27.04.2016)

Einstein-Cartan-Palatini-Holst Lagrangian and equations of motion.

Hamilton analysis of Einstein-Cartan-Palatini-Holst Lagrangian - ADM formalism.

RAQ - Summary of general algebraic approach to quantization of systems with constraints.

Basic loop variables and their representation.

Volume and Area operators.

Charles University | Information system of Charles University |