Loop Quantum Gravity I 1102-4`LQG
1. classical elements
Gravity in connection-frame variables, Plebanski action, Ashtekar complex variables, Holst action, constraints and gauge transformations, canonical formulations, new viewpoint on gauge transformations, time and deparametrization
2. Elements of quantum canonical theory: kinematics
a) gravity
diffeomorphically invariant quantization of the gauge theory with compact gauge group, problems with non-compact gauge group, real Ashtekara-Barbero variables, holonomy and flux operators, quantum geometry of initial data and its operators, spin networks
(b) matter
LQG-compatible quantisation of matter, scalar, gauge and fermionic fields
3. Elements of quantum canonical theory: dynamics
constraints and their operators, different approaches, dynamics, solution construction methods
4. Isotropic homogeneous quantum spacetime model - the universe
5. Quantum model of spherically symmetric spacetime - black hole
Type of course
Prerequisites (description)
Learning outcomes
learning outcomes: satisfying the need for knowledge, understanding the structure and developing a new perspective on quantisation methods for the theory of the general relativity symmetries, reflection on time problem, the essence of quantisation, functional measures and the algebraic approach to quantisation via *-algebras and GNS, the classical and quantum nature of time in a theory where the canonical Hamiltonian is a constraint.
Assessment criteria
teaching methods used: typical for the physics department
description of class attendance requirements, including the number of excusable absences: in accordance with the physics department regulations, additional requirements will not be introduced
principles of successful completion of classes and the course (including re-sit): active participation in classes, completion of independent work, presentation of an interesting topic
Bibliography
list of literature related to the subject: "Handbook of Quantum Gravity", Eds. C. Bambi, L. Modesto, and I. Shapiro, Springer Singapore, expected in 2023, and its chapters available in arxiv
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: