|
|
Model Problems of the Theory of Gravitation
Pilc, Marián ; Bičák, Jiří (advisor) ; Langer, Jiří (referee) ; Balek, Vladimír (referee)
Title: Model Problems of the Theory of Gravitation Author: Marián Pilc Department: Institute of Theoretical Physics Faculty of Mathematics and Physics Supervisor: prof. RNDr. Jiří Bičák, DrSc., dr. h. c., Institute of Theoretical Physics Faculty of Mathematics and Physics Abstract: Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action of the Einstein-Cartan theory are derived. Ad- ditional gauge freedom is geometrically interpreted. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still present as part of gauge freedom. 3+1 decomposition introduces tangent Minkowski structures hence Hamilton-Dirac approach to dynamics works with Lorentz connection over spatial sec- tion. The second class constraints are analyzed and Dirac bracket is defined.Reduction of phase space is performed and canonical coordinates are introduced. The second part of this thesis is dedicated to quantum formulation of Einstein-Cartan theory. Point version of Einstein-Cartan phase space is introduced. Basic variables, crucial for quan- tization, are derived via groups acting on the phase space and their selfadjoint represen- tation is found. Representation of basic variables of Einstein-Cartan theory is derived via infinite...
|
|
|
Probabilistic Spacetimes
Káninský, Jakub ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
Probabilistic Spacetime is a simple generalization of the classical model of spa- cetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a generalization is a possible application in the context of some quantum gravity approaches, na- mely those using the path integral. It is argued that this model might be used to restrict the precision of the geometry on small scales without postulating discrete structure; or it may be used as an effective description of a probabilistic geometry resulting from a full-fledged quantum gravity computation.
|
|
|
Lorentz group and its application in the theory of quantum gravity
Pejcha, Jakub ; Pilc, Marián (advisor) ; Krtouš, Pavel (referee)
In this thesis we are dealing with basic methods of theoretical physics focusing on quantum theory of gravity, that are: Hamilton-Dirac formalism for singular systems, Dirac`s method of quantizing systems with constraints and its mathematical formulation - refined algebraic quantization, representation of compact groups and representation of Lorentz group. We apply these methods to find eigenstates of Lorentz group and General linear group generators. We construct a physical Hilbert space on temporal part of 3+1 decomposition of Einstein-Cartan theory. Powered by TCPDF (www.tcpdf.org)
|
|
|
Model Problems of the Theory of Gravitation
Pilc, Marián ; Bičák, Jiří (advisor) ; Langer, Jiří (referee) ; Balek, Vladimír (referee)
Title: Model Problems of the Theory of Gravitation Author: Marián Pilc Department: Institute of Theoretical Physics Faculty of Mathematics and Physics Supervisor: prof. RNDr. Jiří Bičák, DrSc., dr. h. c., Institute of Theoretical Physics Faculty of Mathematics and Physics Abstract: Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action of the Einstein-Cartan theory are derived. Ad- ditional gauge freedom is geometrically interpreted. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still present as part of gauge freedom. 3+1 decomposition introduces tangent Minkowski structures hence Hamilton-Dirac approach to dynamics works with Lorentz connection over spatial sec- tion. The second class constraints are analyzed and Dirac bracket is defined.Reduction of phase space is performed and canonical coordinates are introduced. The second part of this thesis is dedicated to quantum formulation of Einstein-Cartan theory. Point version of Einstein-Cartan phase space is introduced. Basic variables, crucial for quan- tization, are derived via groups acting on the phase space and their selfadjoint represen- tation is found. Representation of basic variables of Einstein-Cartan theory is derived via infinite...
|
guest ::
