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
Course coordinators
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