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.
Last update: doc. RNDr. Karel Houfek, Ph.D. (13.05.2022)
Smyčková kvantová gravitace je jedním z kandidátů na teorii kvantové gravitace, která je nezávislá na pozadí a
nepotřebuje renormalizaci. Hlavním úkolem přednášky je porozumět její kinematické formulaci. Vycházeje z
Einsteinova-Palatiniho-Holstova lagranžiánu provedeme jeho klasickou hamiltonovskou analýzu. Budou
zavedeny Ashtekarovy proměnné a smyčková reprezentace. Je použit Diracův přístup pro systémy s vazbami a
algebraické kvantování. Budou zkonstruovány operátory objemu a plochy, které mají diskrétní spektra. Přednáška
je určena pro pokročilé studenty Mgr a PhD studia.
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 (http://arxiv.org/abs/gr-qc/0404018)
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 (http://arxiv.org/abs/gr-qc/9504018)
A.Ashtekar, J.Lewandowski : Representation Theory of Analytic Holonomy C* Algebras,
in Knots and Quantum Gravity (ed. J.Baez, Oxford U.Press) (http://arxiv.org/abs/gr-qc/9311010)
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 (http://arxiv.org/abs/gr-qc/0404018)
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 (http://arxiv.org/abs/gr-qc/9504018)
A.Ashtekar, J.Lewandowski : Representation Theory of Analytic Holonomy C* Algebras,
in Knots and Quantum Gravity (ed. J.Baez, Oxford U.Press) (http://arxiv.org/abs/gr-qc/9311010)
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.
Last update: T_UTF (27.04.2016)
Einsteinův-Cartanův-Palatiniův-Holstův lagrangián a pohybové rovnice.
